The chances of getting into a big City Investment Bank are lower.
That said, if you cannot get into a top 5 university, don't stress yourself. Do VERY well academically wherever you go and try to shine on the extracurricular stuff too. This will help you to stand out when you apply to City firms.
i went to Kent, and also did a couple of the business school modules in my time. It depends what sort of role you are after tbh. One of my interviewers at Citi went there and is now a project manager and I also found a place at Citi as a Software Engineer. It would suprise me if, after doing well, you couldn't get some form of job but I would expect you will find the top end roles hard to come by.