You're right that you needed 60/80 UMS but you need to understand that this doesn't mean you needed 60 marks in the exam as the grade boundaries determine how many UMS you get, not your marks alone.
Whatever mark out of 80 they set as the grade A boundary gives you 64/80 UMS (as it's always 80%) and whatever mark they set as the grade B boundary gives you 56/80 UMS (as it's always 70%). The mark you need is halfway between these two grade boundaries. So if they set the B grade boundary at 40/80 and the A grade boundary at 50/80 you'd need 45 marks in the exam to get 60/80 UMS (in reality the boundaries are likely to be higher than that judging by previous years' but you get the gist).
From GCSE to A level, it's all changing