Returning to this thread briefly as I had some additional thoughts over dinner. "Going up" (a term which refers to enrolling at an Oxbridge college) at age 21 isn't implausible at all because there weren't particular ages for going to one school or another back then as there are now.
To use a few randomly selected examples, Lord Byron went up in 1805 aged 17. Thomas Bodley, after whom the Bodleian Library at Oxford is named, went up to Magdalen aged 15 and received his B.A. aged 18, granted that was in the 16th century so nowhere near your time period. On the other side of the coin, Thomas Hardy's friend Horace Moule, who has been suggested as the inspiration for Jude the Obscure, didn't go up to Queen's, Cambridge, until he was 22, and didn't get a B.A. until he was 35.
So don't get too hung up on how old he is.
On the question of whether he would go to Oxford, and if it were realistic to do so, Hardy's Jude is actually a good point of reference. All the action of the novel begins because Jude desperately wants to go to the university and learn things, just to study and to acquire knowledge. So Oxford did stand, for some people in your time period, as a symbol of the pure acquisition of knowledge. If a mother wanted her son to be a learned scholarly man, she would quite conceivably want him to go there... Whether he would be able to get there may be another matter.
