Last week, it was the Education Secretary, Michael Gove.

Yesterday, it was the Labour leader, Ed Miliband, and today it will be the Deputy Prime Minister and Liberal Democrat leader, Nick Clegg. All, in their different ways, are seeking a solution to one of today's most pressing conundrums: how to reverse this country's shocking and stubborn decline in social mobility. Yet all, in their different ways, are also fighting shy of an obvious answer: taking another look at grammar schools and selection according to academic ability.

It is easy – especially for those who benefited from them – to wax nostalgic about grammar schools. They extended opportunities to bright children from modest backgrounds, children whose families in most cases not only lacked the means for private school fees, but would never have dreamt of paying. Many of those children rose to become the senior professionals – the politicians, academics, civil servants, scientists – of the latter 20th century. They made the country's premier universities, and Parliament, more socially mixed than they were before and probably have been since.

But as Mr Gove pointed out, the dominance now exercised by those educated privately constitutes "a deep problem" in our society. It simply cannot be that those whose parents paid for their schooling are so much better and brighter than the state-educated majority. It can be, regrettably, that many of them enjoyed a better education, or at least one that equipped them better to advance in post-school life.

It could be objected that by no means everyone aspires to go to Oxbridge or become a senior judge, an ambassador, or even prime minister. But the persistence of the old school tie in these fields – despite often heroic efforts to broaden entry – strongly suggests that the pool of those who might harbour such ambitions is far too narrow. Grammar schools helped to widen that pool. But progress has not been maintained. Comprehensives were introduced with the best of intentions and have notched up successes. But they are failing the very pupils so well served by grammar schools: academically gifted children from poorer families, who now have no escape from the diktat of house prices and catchment areas.

The introduction of academies by New Labour, which has been accelerated by the Coalition and supplemented by free schools, was an admission that comprehensive schools were not always and everywhere the answer. Yet all the experimentation now in train eschews the one thing many parents most crave: selection by academic – as opposed to musical, artistic or sporting – ability. This remains taboo, so much so that the chief objection voiced by opponents of free schools is that they will become grammar schools by another name.

There was, of course, a double downside to grammar schools: rigid selection at 11, which branded a majority of pupils failures, and the substandard education at many, though far from all, secondary moderns. This shows what else needs to be done if grammar schools are to return: perhaps a higher age for selection, with the flexibility to transfer at any age, and a radical improvement in the quality of technical and vocational education, so that pupils leave with recognised, and respected, qualifications.

That Britain needs to increase social mobility, and urgently, should go without saying. The issue is not just one of social justice and cohesion – though these are important in themselves – but one of squandered talent and unfulfilled lives. For the sake of those who would surely benefit from a more academic education, the ban on opening new grammar schools and selection by academic ability should be revisited.