(There's a pie chart at the bottom which combines the PMs and Chancellors. The following shows how it was counted).
The first, Rab Butler, was already in office when The Queen arrived.
1 R. A. Butler Cambridge, Pembroke
2 Harold Macmillan Oxford, Balliol
3 Peter Thorneycroft Royal Military Academy, Woolwich
4 Derick Heathcoat-Amory Oxford, Christ Church
5 Selwyn Lloyd Cambridge, Magdalene
6 Reginald Maudling Oxford, Merton
7 James Callaghan Didn't go to Oxford - sat civil service exams instead
8 Roy Jenkins Oxford, Balliol
9 Iain Macleod Cambridge, Gonville and Caius
10 Anthony Barber As a PoW, law degree via the Red Cross, then Oxford, Oriel
11 Denis Healey Oxford, Balliol
12 Sir Geoffrey Howe Cambridge, Trinity Hall
13 Nigel Lawson Oxford, Christ Church
14 Sir John Major Didn't go to university - took banking exams
15 Norman Lamont Cambridge, Fitzwilliam
16 Kenneth Clarke Cambridge, Gonville and Caius
17 Gordon Brown Edinburgh
18 Alistair Darling Aberdeen
19 George Osborne Oxford, Magdalene
Chancellors of the Exchequer
The totals for provision of Chancellors of the Exchequer
Oxford 8
Cambridge 6
Other universities/colleges/professional exams 5
Other universities/colleges/professional exams 5
Oxford would have had 9 because Jim Callaghan would have gone there if he'd had the money, although which college is not known. Balliol scores 3, ahead of Cambridge's Gonville and Caius with 2.
To combine that with the previous bouquet of prime ministers it must be remembered that you get different answers depending on whether you count the number of offices (because some people served as both PM and Chancellor) or the number of administrations (because some people got more than one term).
Prime Ministers
Totals for the provision of Prime Ministers (inc. Nick Clegg )
Oxford 8
Cambridge 1 (Nick Clegg)
Other universities/colleges/professional exams 4
Other universities/colleges/professional exams 4
Combined Totals
A crude combined total is to add the two counts, which means some people will be double-counted such as Harold Macmillan, who served as PM and Chancellor, while Harold Wilson, Margaret Thatcher and Tony Blair will have their multiple terms under-represented. It will give the general proportions although it won't be numerically accurate. I've included Nick Clegg, so consider Cambridge slightly over-represented if you wish, but the effect is negligible.
Combined provision of colleges to office:
Oxford 16
Cambridge 7
Others universities/colleges/professional exams 9
Cambridge 7
Others universities/colleges/professional exams 9
Dominance of Balliol
Despite the fiddle-factor it is still worth looking at the dominance of Balliol, but bear in mind that a weighted count would give St John's (Blair) and Somerville (Thatcher) more prominence.
Office holders educated at Oxford
1 Anthony Eden - Balliol
2 Harold Macmillan - Balliol
3 Sir Alec Douglas-Home - Christ Church
4 Harold Wilson - Jesus
5 Edward Heath - Balliol
6 Margaret Thatcher - Somervillle
7 Tony Blair - St John's
8 David Cameron - Brasenose
9 Derick Heathcote-Amory - Christ Church
10 Reginald Maudling - Merton
11 Roy Jenkins - Balliol
12 Anthony Barber - Oriel
13 Denis Healey - Balliol
14 Nigel Lawson - Christ Church
15 George Osborne - Magdalene
Of the Oxford colleges, Balliol is the front-runner with 5 but Christ Church is chasing it with 3. At Cambridge, Gonville and Caius also scores three.
Oxford colleges
Balliol 5
Christ Church 3
Others 7
Conclusion
It is surprising that Oxford has retained its dominance given the competition from Cambridge and ancient universities such as Edinburgh. Besides, universities such as Durham were established in the early Victorian period and many of the Red Brick (i.e early 20th Century universities) have had a century to catch up. Even the Plate-Glass universities have been in business for about 50 years.
Even more surprising is that it has dominance over Cambridge which outclasses it in some technical subjects.
Approximate proportions of higher education of PM and Chancellor of the Exchequer