Oxford is the city of dreaming spires; Cambridge, of perspiring dreams. So goes the old joke – and in truth, although these two universities are indelibly linked in the common imagination, they really are quite different in character. Oxford is florid, confident in its superiority, hyper-traditional, a technicolor social scene of outsize personality politics, expressed in the Bullingdon Club, Rhodes Must Fall, Oxford Union tribes.

Cambridge is its arriviste cousin (founded by monks fleeing persecution in Oxford), a little smaller, in drab and flat fenland, more neurotic, with a quirkier variety of mock-historical architecture (Downing: neo-classical; Corpus Christi: mangled neo-Gothic; Murray Edwards: space-age chic), the home of drier kind of intellect – analytical and dominated by the sciences – and, in summer, a place of beauty unmatched in England – filigreed spires, sunlit avenues and wide skies reflected in the river Cam.

What they share is a troubling level of elitism – over the past three years, eight top schools in the UK have got as many pupils into Oxford and Cambridge as three-quarters of all other schools and colleges put together, according to figures collated by The Sutton Trust, an access charity. Access outside the high-performing state schools of the South East was particularly poor, with only 0.8% of HE applicants from the North or the Midlands applying to Oxbridge.

Lord Adonis, one-time intelligent voice on public sector reform turned Twitter addict, recommended in The Guardian earlier this week that Oxford and Cambridge should establish new colleges with a remit to “significantly increase the number of places available for students from schools and families without an Oxbridge tradition”.

“Over time, they might also transform the culture of the two universities,” he argued.

There are several reasons why that is a bad idea. It will do nothing to break down one of the most insidious features of the Oxbridge admissions system: informal contacts between top private schools and particular colleges, which distort the ostensibly meritocratic admissions process.

Access isn’t just about giving more places to state school kids – it should promote a vision of the university in which state school kids are not only free to do their best in an academic setting but to shape social life for the better, and to change its rules.

One of the most grotesque features of modern Oxbridge is the extent to which, in the absence of a real diversity of class backgrounds, much of university social life is dominated by endless forms of middle class one-upmanship – a toxic grievance culture, in which “coolness” is measured in performing at disadvantage. The products of London state schools with very strong Oxbridge records lord it over poshos from private schools out in the sticks; well-heeled private school kids garner social cachet by playing at “grime chic”, pairing signet rings with tracksuits, aping working-class culture à la eighties-style mockney.

Creating new colleges would do little to change that. First off, unless the colleges of the historic centre are repossessed, sites would have to be found on the periphery. There is already a kind of geographic snobbery about colleges far out from the centre in any case: “Girton is miiiles away” goes the jibe (fifteen minutes by bike).

It is far more sensible, surely, to increase capacity in the already existing colleges and improve links with the 3,000-odd state schools.

Adonis argues that setting up new colleges would be “in the tradition of Oxbridge colleges set up for women”. The comparison is compelling, albeit flawed. Explicit bars to entry can be overturned overnight, but the heart of the access problem is that the Oxbridge system, while giving the illusion of full meritocracy, has ended up cementing invisible brakes on working class aspiration and has created a gross undergraduate culture of middle-class game play. Breaking that nexus will take time and patient effort.