I know my post might spark controversy, but it's a reflection of my experience as a mechanical engineering graduate from a russel (non-oxbridge uni), and the experiences of some of my coursemates. My response is mainly relevant if you're looking at engineering. I'm currently in full time employment as a grad mech engineer on a grad scheme, but a good number of my classmates are either unemployed or employed but not in mech engineering.
Now in response to your post, it all really depends on what you want to get out of the uni degree/experience.
If it's purely love for the subject and trying to learn as much about it as you can, then defo go for an oxbridge degree. Especially at Cambridge where it's not just mech eng, but all engineering fundamentals mashed up in one big course. You can still live in student accomodation whilst in your hometown just to get the "student experience" if it's that high up your priorities.
Similarly, if your point is to do research after your degree and/or stay in academia, then an oxbridge degree will be a huge plus to get into those. And will give you the right background to succeed in them.
On the other hand, if your point from the degree is employability, and you're 100% sure you would like to become say a mechanical engineer working in industry, then don't go to oxbridge! Lower ranked unis are so much better for engineering employability. According to unis stats:
Uni of Cambridge employability for MEng Engineering:
67%Uni of Oxford employability for MEng Mechanical Engineering:
55%Uni of Brighton employability for MEng Mechanical Engineering:
90%Engineering for the purposes of working in industry needs a lot less theory and more practice. So going to a lower uni gives you just enough theory that you need, and leaves you free time to go look for real life experiences in industry, which is what would make you more employable. On the other hand, an oxbridge degree is so heavy with theory - that you will use very little of, once on the job - that it eats up all the 4 yrs you spend at uni, and you'd never find time to look for job experiences and/or do them.
I understand my post isn't directly related to your question, as is raising a different matter, but thought I'd share my personal experience.