It might have been instructive to put that question to the audience, once they had calmed down. If 20,000 is too little, what is the right number for Britain? Cumberbatch spoke of 11 million refugees from Syria. How many should we take, in all decency? 200,000? Half a million? I think at that point there might have been a certain amount of shuffling in their seats. Some people might have discovered some fascinating and overlooked detail in their theatre programmes.

The truth is that good people are capable of two inconsistent desires in their hearts. They are perfectly capable of being simultaneously indignant at the slowness of politicians to take more migrants fleeing Middle Eastern war zones, and alarmed at the failure of politicians to cope with the consequences of the rapid and unforeseen growth in UK population. As we learnt last week, the population of this country is set to grow by another 4.4 million just in the next 10 years. It is going to hit 74.3 million by 2039 – 80 million by 2050.

That is an astonishing change, when you consider that Britain was only about 54 million when I was born. This boom is in many ways a compliment to this country – the most dynamic economy in Europe, the place people want to be, where ambitious and energetic people can see a future for themselves. And yet you could not argue that this fundamental change represents the settled will of the British people – and especially not when 51 per cent of that demographic expansion is to be caused by immigration.

The reason people get so aerated about this issue is that they feel politicians have somehow tricked them. First there was the Labour Party that decided in the late 1990s to take the brakes off immigration, and to turn a blind eye to illegals, for the utterly cynical reason that they believed that immigrants were more likely to vote Labour. That conspiracy, for obvious reasons, was not explained to the public at the time, though some Labour people have since fessed up.

Then there has been the general failure of government since to get a grip on the numbers – in spite of repeated promises to do so. It is a painful truth that we said we could cap immigration in the “tens of thousands”; and yet this year alone we have had net immigration at 330,000. It is no wonder, when you have your natural fecundity rate turbo-charged in this way, that we have been struggling to catch up with the homes and the transport infrastructure that we need.

Now, I am not remotely pessimistic about our future, and with care and imagination we should be able to find the space. For all the talk of a Northern Powerhouse, Manchester is still a third smaller than it was in 1931. And I am not sure that we want the opposite problem – a falling population. In Japan they are going to plummet, over the same period, from 125 million to 90 million. They buy more nappies for old people than for babies, and have more pet dogs than kids under 15. People understand the problem of an ageing population, and the need to pay for pensions and to keep the economy moving; indeed, most people are prepared to support some level of immigration, provided it is controlled.

But it feels at the moment as if there is a giant plot – abetted by big business and tacitly supported by the forecasters in the Treasury – to use the excuse of EU rules to keep immigration beyond democratic control, so that the numbers keep rising, and so British companies get the skills they need; and all the while politicians can limply claim there is nothing they can do, except perhaps for some misguided and counter-productive restrictions on student visas. It won’t wash. There may be a case for immigration; there is no case for a lack of control. Cumberbatch was right to bash us politicians – but not for the reasons he gave.