Although post-FY2 specialty applications do have your medical school written on them, it's not a selection criteria.
Applications are still scored against objective criteria in about 10 different categories - there's a certain number of points available for additional degrees, prizes, publications, audit, teaching, commitment to specialty etc, and the criteria for scoring are very clear. Which medical school you went to is not included in any of this, so there is no chance of bias at the pre-interview stage.
Even the interviews are standardised as far as possible - often multiple stations with different panels and different aims (I had to do a presentation, a clinical scenario and a portfolio station). Although there might be the tiniest chance of your university impressing someone in the portfolio station, the difference it could make would only be marginal as the mark schemes are quite rigid.
At consultant level, I think things are more flexible, but by that point you'd have been a doctor for at least 10 years, usually more, so it really is pretty irrelevant.