I have done some limited searching and to date it would seem so. However there are some very learned people on this site who will know if you are correct or not.
John Stuart 3rd Earl of Bute 1762-3 studied at Eton and the University of Leiden in The Netherlands.
Lord, later Earl John Russell 1846-53 and 1862-63 was educated at Edinburgh University
Neville Chamberlain 1937-40 was educated at Mason Science College which later became the University of Birmingham.
Thanks for answers so far, it does seem that Brown will be the 3rd PM educated at a university that is not Oxford or Cambridge. Not counting Neville Chamberlain as MSC was not a university at the time. Also worth noting that there is still no British PM who went to an English university that is not Oxford or Cambridge.