I've applied to LSE with 3A* as my predicted grades for A Level, and haven't still received an offer. I guess it depends on the subject choices you've chosen for the course. I have taken Chemistry, Accounting and Maths (seeing as LSE asks for sciences and maths, with accounting) for the Accounting and Finance course. My teachers and friends also said I've written an amazing personal statement, one that my Exam Co-ordinator praised very much. Plus my reference was top-notch, and LSE's still hesitating with any offer.
To answer your question though, I've not heard of any university changing their decision seeing your actual grades. Hope you get that City offer, man. Got mine's like a month ago - A*AA required.