Mr Johnson said that there was no reason why state school pupils should also benefit from several hours a week of physical education.
He went on: “I think the Government totally understands people’s appetite for this, they can see the benefits of sport and what it does for young people. I think they understand very, very clearly the social and economic advantages.
“I think it is of profound importance for the happiness and success of this country that we have more sport in schools.”
“I would like to see a much more thoroughgoing effort. I think we must build on the achievements of these Games.
“People are signing up for sporting activities of all kinds, they are enrolling, they are involved.”
Mr Johnson echoed a suggestion made by Mr Cameron that the 80,000 volunteer Games Makers at London 2012 could “mobilised” to “train kids up” in sporting activities, given that they have already been checked for criminal convictions.
Ed Miliband, the Labour leader, took to Twitter to criticise the Government’s decision to scrap the two-hour target.
He said: Just met former school sport coordinator for Southwark. He organised competitive sport for schools but lost his job. Not his fault or school’s.
“Southwark school sports coordinator also told me schools have now told him they are doing much less because of loss of support.”
But Jeremy Hunt, the Secretary of State for Culture, Media and Sport told BBC Radio 4’s PM that targets were not the answer to improving participation in sport in schools, saying this was “not all about money and structures, but a culture change that recognises the power of competitive sport.”