I am also a hopeful medical applicant but am in a different situation to you...
The score "2770" is actually quite a good score, like it is better than the general average which is around 2400 (600 per section) and most UKCAT universities would consider you with a score like that. But I would avoid universities that only take the best "lets say 500" as it may be quite difficult with that score... But yeah, to be honest, if thinking of applying to Cambridge, I would look at your UMS and if they are all around 90% and up I would personally go for it and just try hard for the BMAT, maybe not Oxford since they would prefer 80%+ of GCSEs at A* grade, which you have pretty much got. But I would think that you have a very good chance of getting into most other universities with those grade to be perfectly honest... But hey, that is my opinion and others may disagree...