Your STEP score matters a lot. You need 1 in both STEP I and STEP II.
Though Oxford is way better for CS.....(lesser no. of seats, lot of interaction with your tutor,very very theoretical as compared to Cambridge,more 'reputed').
A*AA is more like a predicted requirement. You need an A*A*A in reality as colleges usually do not give offers below 40 IB points (which translates to A*A*A and not A*AA). Getting an offer is not the same as being accepted to read CS.