Differences in Difficulty of Recruiting Process Between Cities?

In a few months I'll be applying to Summer and Off-Cycle analyst programs in EMEA, and had doubts about the difference in competitiveness in the recruiting process between London and the other European "finance capitals".

Is there a difference between London and Frankfurt, Paris, Madrid, Milan, Stockholm...etc when it comes to recruiting?

I come from one of those cities, although I am not doing my undergraduate studies in that city, and wanted to know if my chances would be different in London or my home city.

I'm an undergrad at a "non-UK target" school (ESSEC, Bocconi, St. Gallen, CBS, SSE...) so I know already that my school is not at the top of UK recruiters' lists (vs Oxbridge, LSE, Warwick, Imperial...) while still not being in a completely irrelevant school.