For reference; A guy in my school (Class on 2015) got into Cambridge for Computer Science and Mathemarics (not even a full on mathmo). His IGCSE's were of course all A*'s with 96 UMS average. At As (of which he did 6) he got all A's at again 96 UMS average (598/600 for maths and further maths at As; full marks in Physics and Computing). In A2 he got his interview and offer (A*A*A with 1 1 in STEP II III). Results were 4A*'s and an A (because he self taught the rest of Exonomics a level for fun) with 95 UMS and 1 in STEP I and III and 3 in STEP II.
I would say, having sat STEP 1 this year, that it is the biggest challenge. 2 and 3 are the worst. I am not saying you're not good enough, anyone is if they work like there's nothing more to life (and/or if they are a genius), but it is worth overthinking what you want you university experience to be. The workload in Cambridge especially for maths is astounding, sleep is a unrecommende day option according to the guy mentioned above (he feels stupid there). I was often asked why I didn't go for Oxford or Imperial, that's because my long term plan is to ease into Uni maths and eventually get a post grad masters in Oxford (or Imperial). That's just me though.
Hope the example helps
P.S. I got 90 UMS in maths and further at As along with 3 more A's. Applied to UCL, Bath, Durham, Bristol and St Andrews (the last 3 being my insurances/least likely choices) and guess what? Only UCL and Bath sent me offers (unis with highest grade requirements of my selection); only reason my teachers came up with is they thought I would reject them anyway. So don't underestimate yourself.
Be smart about your choices.