While it's hard to get an offer from a non-target university in the London office, it's not at all impossible (from personal experience as well as the experience of those around me!).
I suspect that your CV could do with strengthening. The firms are looking for people who excel in what they do - you need to be able to demonstrate this. You need a killer resume which clearly lays out, with statistics, what you’ve done which is extraordinary. Things like:
- What degree classification are you expecting to graduate with? Are you top of your class? How have you demonstrated the qualities that they’re looking for in your course? Things like leadership, entrepreneurialism, analytic capabilities
- They’ll want to be assured of your academic capabilities. Have you sat any other standardized tests (GMAT, GRE etc) If so and you’ve done well (top 5th percentile) then add this in
- What have you done outside of your studies? Have you led a club? Started a club or endeavour of some sort?
- What work experience do you have? Have you gone above and beyond what is expected of you at work?
It’s also worth getting to know the recruiting team. If I were you I'd drop them a message saying that you're disappointed that you weren't successful in your application to the one day event, but interested in the firm and would like to know more. Attach a copy of your (super strong!) CV and ask what events they have coming up and if you'll be able to meet with them. In my experience knowing someone in recruiting goes a long way - and is an easier relationship to cultivate than with a partner.
Good luck - and let me know if you need any help!