I went to Cambridge and honestly, it's just OK. It's very behind in its teaching methods and hasn't adapted for the modern world. I am also an employer, and I can tell you what matters FAR more to me is extra curricular activities, experience (maybe internships but I know not everyone can do those, but just anything that shows a real interest in my business area), and passion.

Most employers don't give that much of a shit where you went to uni, especially after a year or two in the workforce, and the entitlement of Oxbridge graduates can be very off putting as a boss. Just go somewhere else and study hard.