I think that before you make any choices do work experience in a law environment.
As a law undergrad I believe I made the wrong choice in degree, I am undecided about career. Law is a fascinating degree, but it is competitive, very hard work and getting a 2:1 is not as easy as people think, and if you want a career in law, you need at least a 2:1.
Now I'm not saying it is easier to get a 2:1 in other degrees, I'm merely explaining that with my 2:1 this year, I was reading about 25 + chapters of long books a week as core/research etc, as well as reading through legislation and cases. Which is what you should expect, but for a career in Law, they want you to have a 2:1, proof your well rounded e.g. sports, the arts, interest in charity and the community, work experience in law, a job in general, taking an active part in your course etc. and even then you may well not be a top candidate.
Take me for example, Law degree currently: 2:1, I work with disabled children, I volunteer at my local hospital, I am part of the volleyball team and I take part in choir. I also write for my law school newsletter, am I first year undergrad mentor, have had many many work experience placements and I am consistently at networking events. I also learn mandarin part time.
I literally have no hours left in the day.
My cousin however, who did all of the above and volunteered for cab, did an English degree and she got a training contract with a magic circle firm who sponsored her GDL, LPC and she is now in her second year of her training placement, currently seated with project finance. She seemed to have more time than me as her degree was seemingly more well balanced with the level of work expected off of her.
At oxbridge the expectations of you are worse, and it may be worth considering whether it would be harder to do well as a result. But do go to a top russell group university, but don't forget to study which uni on the student surveys, to decide which would best suit you, e.g. Southampton Uni ranks 128th on exam feedback, as a result my friend studying law there feels like the undergrads are fishing around in the dark, as the new policy is not to give feedback unless you fail.