Contrary to some recent commentary, grammar schools do exist in Scotland.

University friends of mine went to Aberdeen Grammar School, where Lord Byron and Robin Cook were pupils; former colleagues attended Lanark Grammar, while prominent Scots such as Fred Goodwin and Andrew Neil are Old (Paisley) Grammarians.

These, however, are grammar schools in name only. All – along with those in Dunoon, Hamilton, Perth and Musselburgh – function within the state sector. Only Glasgow’s Hutchesons’ Grammar School (which produced the MSPs Humza Yousaf and Anas Sarwar) forms part of Scotland’s larger-than-acknowledged independent sector.

So grammar schools in the English, Welsh or Northern Irish sense are alien in Scotland, something that helps fuel our potent educational mythology, that private (or selective) education is largely an English phenomenon; that most Scots attend good local schools; and the most complacent, that we possess “the best education system in the world”, a notion regularly undermined by Scottish Government statistics.

Sure, while seven per cent of the UK population is educated privately the Scottish figure is slightly lower at five per cent, but that’s hardly worthy of smugness given the extent to which both percentages dominate university admissions and professions north and south of the Border.

Even grammar-type selection isn’t unknown in Scotland. My mother is one of five children raised in a working-class part of Edinburgh, and before comprehensivisation began in the late 1960s, all of them were tested aged 11 and sent either to Broughton High School or what was then called Bellevue (now Drummond). This was a common story across the country at that time.

It was undoubtedly a divisive system, mirrored by the 11-plus south of the Border, which is why the Prime Minister’s hazy plan for a new generation of grammar school has received so much criticism. And it’s come not just from the usual suspects on the Left, but from within the Tory tent: former education secretary Nicky Morgan recently got stuck in, while “two brains” Lord (David) Willetts warned that grammars “tend to be captured by the better-informed, more affluent parents”.

A section of the Conservative Party, however, has long been obsessed with the system that catapulted them from the Home Counties to Oxbridge and then on to Parliament, but it rests on an unhelpful English myth, that grammar schools once helped boost social mobility among gifted working-class children and could, therefore, do so again.

But there’s precious little evidence that any of that is true. Even in their heyday grammar schools educated relatively few pupils from disadvantaged backgrounds, as remains the case with those that survive to this day (only three per cent, for example, claims free school meals). And as the economist Thomas Piketty demonstrated a few years ago, the number of people in higher or middle occupations increased after the war not because of social mobility but because there were larger numbers of those jobs available.

Mrs May is a case in point: her grammar school didn’t rescue her from some sink estate in the north of England, rather it transported her from an already relatively comfortable background (her father was a vicar) to Oxford, where in truth she already had a reasonably good chance of ending up. On this point the Prime Minister was airily dismissive in her speech last Friday, arguing that “people get lost in the argument about whether the grammars schools of the 1950s and 60s improved social mobility or not”, as if that were an adequate counter-argument.

She also tried hard to pre-empt all the usual critiques of grammar schools, but didn’t quite succeed. Mrs May acknowledged, for example, that wealthy families dominate access to certain schools through “selection by house price”, but beyond asking new grammars to “demonstrate” they’ll attract pupils from “different” backgrounds, Mrs May identified no tangible way of preventing it. She also mentioned the problem of those same families paying tutors to help their children get through the 11-plus, but her only solution was some waffle about employing “much smarter tests” to guard against it.

Then that unfortunate word “meritocracy” reared its simplistic head. Like Nicola Sturgeon, Mrs May appears not to have actually read Michael Young’s satirical book, “The Rise of the Meritocracy”, and has therefore missed the rather important point that it’s not meant as a good thing. The Prime Minister’s mantra is transforming the UK into the “great meritocracy of the world”, but as Young convincingly argued several decades ago, selective education ends up consolidating inequality rather than increasingly social mobility.

Indeed, the belief certain Tories have that grammar schools promote social mobility is like the faith lots of Scottish Nationalists have that free tuition widens access to universities. All the empirical evidence suggests the reverse is true, yet both policies remain stubbornly resistant to the facts, while respective naysayers are regarded with contempt. And the central problem with each is also analogous: rather than boosting social mobility, grammar schools and free tuition end up disproportionately benefiting the middle classes – who already do pretty well in educational terms.

In last week’s Programme for Government, the First Minister reiterated her intention to “protect” (from whom?) free university tuition, but there were more welcome developments in other respects. Not only did Ms Sturgeon confirm a “major review of student support” (which is much more important to social mobility than free tuition) but also the continuing implementation of recommendations from the Commission on Widening Access.

These include lower admissions thresholds for students from less affluent backgrounds, what our American friends would call “affirmative action”, the response to which was unintentionally revealing. “Middle classes will be ‘squeezed out of universities’ under plans to increase poorer student numbers warns Universities Scotland” was a recent headline in this newspaper, to which my immediate reaction was: and?

Universities Scotland referred to this as “displacement”, although curiously I don’t recall comparable histrionics about the (considerably larger) displacement of working-class students that’s been happening for several decades. The Commission on Widening Access, meanwhile, uses more diplomatic language, rightly urging the creation of what it calls “adjusted offers” as a vital step towards increasing access.

This policy, however, isn’t trouble free, especially if (like reintroducing grammar schools) it leads to laziness about improving standards in schools serving less-advantaged young people. It could also end up causing problems if based upon post codes rather than individual circumstances. There will be lots of children, for example, attending average schools and from families with no history of university attendance in post-code areas included among the higher quintiles according to the Scottish Index of Multiple Deprivation.

Hopefully the Education Secretary John Swinney is alive to this, although the truth is that real progress on social mobility can only come through major changes to the wider economy and jobs market, but of course that’s much harder for politicians to affect than educational tinkering.

So both the UK and Scottish Governments have their education blind spots, but nothing currently emanating from Holyrood will be nearly as detrimental to social mobility as the grammar school “bring-backery” about to preoccupy Westminster.