Attending Oxford or Cambridge at 13 was not unusual - there was no minimum age at which you could enrol, although younger than 13 would have been uncommon. And of course, you had to be male - women could not take degrees in Britain until the mid-19th century.

The diarist and civil servant Samuel Pepys didn't enrol at Magdalene College, Cambridge until he was 17 (in 1650), but this was in part due to ill health and lack of finances. The thing to remember is that the course of study was both very different and much less formal than it has been in the 20th and 21st centuries - in theory you would study works of philosophy and religion, in Latin, Greek and perhaps Hebrew; but many young men left without taking their degree. A 13 year old and a 19 year old could all be accommodated within this system, even at varying levels of ability and preparation. For a later example of this, consider the 18th century politician Charles James Fox, who went to Hertford College, Oxford, at 15, but left without a degree because he found the work easy and tedious.