Cambridge University seems to have developed in numbers, and therefore the requirement for colleges, as a result of rivalry between students and towns people in Oxford. The first college at Cambridge was actually founded by Walter de Merton - who founded Merton College at Oxford. It seems that this college at Cambridge, called Pythagoras Hall, was created as Walter anticipated students from Oxford moving elsewhere because of the trouble between students and others in Oxford.
The first recognised college at Cambridge was Peterhouse founded in 1284 by Hugh Balsham, Bishop of Ely. The Church of St. Peter without Trumpington Gate was handed over to the college and was re-named St. Peter's College that in turn became Peterhouse. Houses near the church were used by the scholars who attended Peterhouse and in 1286 a hall was specifically built for the college. The college originally consisted of fourteen scholars and three grammar school boys who sang in the church. All the scholars studied Theology - as befitted a college established by a bishop.
"Medieval Colleges at Cambridge". HistoryLearningSite.co.uk. 2014. Web.