Mr Johnson then interjected, saying that the female students Mr Razak was referring to “have got to find men to marry”.

Kate Green MP, Labour’s Shadow Equality Minister, called on Mr Johnson to apologise for his “outdated opinions”.

“Boris Johnson may think his buffoonery allows him to get away with his outdated opinions but this isn’t funny,” she said.

“These comments are insulting to the women across the country and across the world who have gone to university, worked hard and used their talents to get on. He should apologise.”

The Everyday Sexism campaign group tweeted that the remarks were “pathetically archaic, unacceptably sexist and hopelessly out of touch”.

A City Hall source said that Mr Johnson’s comments were “off the cuff” and said they were “clearly intended as a joke”.

“He does not, of course, think that at all,” the source said. “It was completely light-hearted. It has been misconstrued.”

Another official present at the event said there was laughter and groans from the audience following Mr Johnson’s comment, but insisted that it was seen as a joke by the audience.

Mr Johnson met his first wife, Allegra Mostyn-Owen, while studying classics at Oxford.

Mr Johnson last month described David Cameron as a “girly swot” because he got a first class degree in Philosophy, Politics and Economics at Oxford.

The Mayor of London got a 2:1 degree from Balliol College.

The peer had said that, despite backing the plans when Labour was in power, said that he now believed the line to be an “expensive mistake”.

Mr Johnson said: “That is why the Treasury is starting to panic, and the word around the campfire is that Lord Mandelson is actually doing the bidding of some fainthearts in Whitehall who want to stop it now – not the first or second Lords of the Treasury, clearly, but the beancounters.”

Mr Johnson criticised “the whole nightmare of consultation and litigation – and the huge army of massively expensive and taxpayer-financed secondary activities”.

This meant that £1 billion is likely to have been spent on HS2 before a sod of earth was cut.

He said: “It is the environmental impact assessments and the equalities impact assessments and the will-sapping tedium and cost of the consultations.

“Did you know that in order to build HS2 we are going to spend £1billion by 2015 – and they won’t have turned a single sod in Buckinghamshire or anywhere else?

“That is a billion quid going straight down the gullets of lawyers and planners and consultants before you have even invested in a yard of track.

“To understand the prohibitive costs of UK infrastructure, you need to take this haemorrhage of cash to consultants, and then multiply it by the time devoted to political dithering.”

The new estimate comes less than a fortnight after transport secretary Patrick McLoughlin said the projected cost has risen from £33billion to £42.6billion because of a “contingency2 fund to cover the cost of potential problems with the programme.

The Department for Transport said there were significant changes to the line, such as more tunnels to avoid disturbing the environment and those living near the line.

Labour leader Ed Miliband, his shadow chancellor Ed Balls and former transport secretary Lord Adonis are all said to still publicly back HS2.

Current shadow transport secretary Maria Eagle recently branded the project “essential” for Britain’s railways to cope with rising demand.

But the admission by Lord Mandelson has added to the growing fears that the political consensus over HS2 is in danger of being shattered.

The news came as a senior minister suggested that the government should scrap HS2 and spend the money on other transport projects instead.

David Lidington, the Europe minister, whose Aylesbury constituency in Buckinghamshire will be severely affected by the proposed railway from London to Birmingham, has written to Patrick McLoughlin, the transport secretary, detailing concerns over the new route.

Mr Lidington is known to have serious reservations, but his letter is the closest he or any government figure has come to calling for it to be scrapped altogether.

Attempting to clarify his remarks, Mr Johnson said that it was “utterly ludicrous and infuriating” to suggest that he believes women attend university in order to find a husband.

He insisted that he was merely pointing out that when a large number of students are female, you intensify so-called “assortative mating” – whereby people choose to choose a partner similar to themselves.

“Some people seem to have misconstrued something I said at a press conference five days ago, about relative male underachievement in university entrance,” Mr Johnson said.

“It is utterly ludicrous and infuriating to suggest that I think women go to university to find a husband. I was merely pointing out something that I’ve said several times before – that with a graduate cohort 68 per cent female you intensify the phenomenon sociologists identify as assortative mating.”

Kate Green MP, Labour’s Shadow Equality Minister, called on Mr Johnson to apologise for his “outdated opinions”.

“Boris Johnson may think his buffoonery allows him to get away with his outdated opinions but this isn’t funny,” she said.

“These comments are insulting to the women across the country and across the world who have gone to university, worked hard and used their talents to get on. He should apologise.”

The Everyday Sexism campaign group tweeted that the remarks were “pathetically archaic, unacceptably sexist and hopelessly out of touch”.

A City Hall source said that Mr Johnson’s comments were “off the cuff” and said they were “clearly intended as a joke”.

“He does not, of course, think that at all,” the source said. “It was completely light-hearted. It has been misconstrued.”

Mr Johnson met his first wife, Allegra Mostyn-Owen, while studying classics at Oxford.

Mr Johnson last month described David Cameron as a “girly swot” because he got a first class degree in Philosophy, Politics and Economics at Oxford.

The Mayor of London got a 2:1 degree from Balliol College.

But as a general principle it is obvious that both London and other cities would benefit from better and faster connections. The problem, as Peter Mandelson has indicated, is cost. This thing isn’t going to cost £42 billion, my friends. The real cost is going to be way north of that (keep going till you reach £70 billion, and then keep going). That is why the Treasury is starting to panic, and the word around the campfire is that Lord Mandelson is actually doing the bidding of some fainthearts in Whitehall who want to stop it now – not the first or second Lords of the Treasury, clearly, but the bean-counters. So there is one really critical question, and that is why on earth do these schemes cost so much?

Doug Oakervee is a brilliant man to have in charge of HS2, and if anyone can deliver it, he can. But he is dealing with a system of building major infrastructure projects that is holding this country back. Talk to the big construction firms, and they will tell you the problem is not the cost of actually digging and tunnelling and putting in cables and tracks. Those are apparently roughly the same wherever you are in the world.

It’s the whole nightmare of consultation and litigation – and the huge army of massively expensive and taxpayer-financed secondary activities that is generated by these procedures. It is the environmental impact assessments and the equalities impact assessments and the will-sapping tedium and cost of the consultations. Did you know that in order to build HS2 we are going to spend £1 billion by 2015 — and they won’t have turned a single sod in Buckinghamshire or anywhere else?

That is a billion quid going straight down the gullets of lawyers and planners and consultants before you have even invested in a yard of track. To understand the prohibitive costs of UK infrastructure, you need to take this haemorrhage of cash to consultants, and then multiply it by the time devoted to political dithering.

Look at the Turks. They have decided that they need a new six-runway airport at Istanbul, so that they can take advantage of the growing importance of aviation to the world economy. They are almost certainly going to do it for less than 10 billion euros, and long before we have added a single runway anywhere in the South East. Or look at Chep Lap Kok, the airport Doug Oakervee built for Hong Kong. The authorities announced it in 1989 — and opened it nine years later! If you want to get a sense of our sluglike pace in the UK, we announced Heathrow Terminal 5 in 1988, and it took almost 20 years to create; not an airport, just a new terminal, for heaven’s sake (and if anyone thinks the advantage of a third runway at Heathrow is that it would be a “quick fix”, they frankly need their heads examining).

Other countries have clear plans for their infrastructure needs over the long term, and the talent and managerial firepower is being moved from one to the next. We don’t have a plan; we have a list of schemes, each of which causes politicians such heeby-jeebies that they waste billions – literally – in optioneering when what they need to do is decide on the right course and crack on with it. We have proved with Crossrail and the Olympics that we have the expertise to deliver big infrastructure projects. But time is money: we spend far too long on bureaucratic procedures and then enormously multiply that expense by a political failure to blast on with the task in hand.

The result is that we are being restrained from giving this country the improvements it needs at an affordable price. We are like Laocoon wrestling with the serpents, or like some poor bondage fetishist who has decided to tie himself up in knots — and then realised, too late, that he has gone too far. We tug at our bonds with our teeth and pathetically hope the neighbours will come. Of course they won’t! Our neighbours are out there investing in airports, while we are investing in consultants.

The revelations cast an interesting light on Mr Miliband’s professed love of “One Nation”, about which he’s so fond of babbling. If One Nation means anything, it is that a party promises to govern without favour to any sectarian interest. Quite how that squares with being owned by one union, which then supplies the candidates, defeats me.

I’m having a laugh at Labour (who isn’t?) while pointing out the impossibility of being the perfect candidate, to make a point: the selection procedure needs to be reformed.

For while Labour’s problems are of its own making, none of us can claim to be perfect. The Tory process works as follows: interested applicants are assessed by the Parliamentary Assessment Board (PAB), and gain entry to the “list”. Being on this list permits application to seats; but control over the final selection is in the hands of the local, voluntary association. There’s an uneasy dance, often, between Tory central office (CCHQ) and the association officers, but it’s the associations that have the power. It’s their shortlist and their membership will vote for their choice.

Neither aspect of the process works perfectly. The PAB itself is a fair process, I’d say, reminiscent of any other competency-based job interview. I went through it in 2010 because David Cameron opened up the list and I wanted to apply to stand in Brighton Pavilion. To my surprise, I passed.

Brighton Association, it turned out, was able to resist my many charms and the seat was fought by the wonderful Charlotte Vere. After the election, I was told by CCHQ that henceforth I could apply only for “The City Seats Initiative” – inner city seats, where the candidate’s task is to rebuild the association. I politely declined, and came off the list: I’d come to realise that I didn’t have the urge to fight any seat that might have me. I wanted to beat Caroline Lucas, and represent Brighton.

CCHQ meddles like this, because it’s trying to craft a population of candidates to do the party proud. But the meddling never works – whether with the City Seats thing, or the unlamented “A list” (“You look nice! Do you want to be an MP?”) – because no central office can know who will work best in any particular town.

But neither would it do to allow associations total control. By definition, those of us who belong to a party are unrepresentative, because we’ve self-selected ourselves to be activists. It’s quite arrogant to say that no matter how poorly an association might function (some are great, some aren’t) they have the best knowledge of how to determine who should fight an election for the Conservatives.

There’s an answer to this. CCHQ is entitled to run its PAB process. But final selection should be by primary – whether open, postal or electronic, I don’t really care. Anyone on the PAB list, and anyone who is a member of a local association, should be entitled to put their name forward, and all the voters in the seat be given a chance to have a say in the final selection.

Boris Johnson’s mayoral candidacy was selected in this way. Commentators often mention how Boris is “Tory mayor of a Labour city”; no one ever makes the link with the method by which he was chosen for that fight.

The Tory system works quite well, and opening up selection via primaries would just make a good thing better. But imagine what it would do to Labour! Trade unions would have to find another way to subvert our democracy. At least Mr Miliband could say he believes in One Nation, without his words attracting the cold, shocked laughter of disbelief.