Yes for F1 and F2, applications are blinded but surely for jobs after your foundation years, the university you went to will have an effect (albeit a small one) on how favourable you're looked on as an applicant. Why else would they ask for it?
Surely for the more competitive specialities, an Oxbridge/Imperial/UCL/GKT/Barts/Georges (and arguably Newcastle) medic will be
at a slight advantage (just because of the institution they trained at) over another one who was 'equally as qualified' from a different university. Its easy just saying, 'it's all a fair game and everyone is on a level plaing field', but its not really that level. People deciding on your applications are human after all (and not robots who simply tick off boxes) so they will inevitably show some bias towards preferred instituitions which they believe train excellent doctors. Its a competitive field out there, and though people like to hide this, the fact is medical schools adopt their own way of training their doctors (in accordance to the GMC regualtions of course) so all this talk of GMC accreditation really only applies to FY posts which are blinded like has been mentioned. Of course your experiences, exams, extra qualifications, competence etc all come into play when applying for a CT/ST job, but so does the institution you trained at, even if it is to a small extent. To assume it has no effect whatsoever seems a little iffy.
And I bet I'm going to get neg repped for this which really means sod all to me, but this is just my opinion, and also the opinion of others I've talked to years into their specialist training.