Hi, I'm a third-year History student at Lancaster University, and I had a brother and friends go to Oxbridge (and I interviewed at Oxford) and thought I might be able to weigh in on this.
I can understand the appeal of Oxbridge, as they are known worldwide, but the reality is that for many people, the experience is very different to many universities. There is a very intense workload for those universities, most of the people I know that went there studied humanities subjects (philosophy, politics, english lit etc) and they had to complete an essay most weeks, as well as attend meetings to discuss subjects in detail with their tutors. Although this is a style which may suit some people, you should think very carefully whether that sort of workload is something that is going to be enjoyable or whether you would be more suited to studying somewhere where your essays are worth a higher % of the year and completed less frequently. Definitely try reaching out to people at Oxbridge studying the degrees you are interested in and go to open days, which will give you more of an understanding of whether that is a place for you.
You should definitely still apply either way, but also prepare to look at other universities, and definitely go to open days. I love Lancaster, the workload is just right for me and I know I wouldn't have enjoyed going to Oxford as much as I have enjoyed it here. I interviewed at Brasenose, and got called for an additional interview at Lady Margaret Hall, and while I found the content of the interviews interesting, the entire situation was very intense and confirmed what I already thought about my preference for Lancaster.
I am happy to answer any more questions,
~ Georgia