So, here's all I (believe to) know on this topic and some follow up questions: Only the more wealthy (upper and middle class) did have the resources to send their offspring (of course mostly only the sons) to university. They had to pay tuition fees (how much?), but could also get a scholarship.
But I couldn't find anything on how they would apply for university. Did they have to take entrance exams? Where there limited places (did they maybe apply in advance)? Did they have to prove their identity and if so, how? What documents did they need to enroll? (I'm mostly asking that because there are records of women, who presented as men to get into university.)
I suppose there's a lot of change in the 19th century and differences between universities, but I'd mostly be interested in the second half of the century and let's say Oxford University (if specifics are known).