In todays recruitment market, good work experience or internships are essential in setting yourself apart from your peers.
Unfortunately I don't think Birmingham Uni is a key recruitment point for some of the more prestigious companies. Even more reason why you need some really good extra-curriculars on your CV.
When it comes to work experience anything is better than nothing. It's very difficult to get short term work at most consultancies, but they will look very favourably on experience from banks and industrial programme management.
Hope this helps... and good luck!