Original post by DFranklinI'd say it's not so much a question of memorizing it, more doing question after question until it's lodged in your brain. You don't have to know all the formulas (I don't remember all the trig integrals, nor the details of the trig factor formulas), but you need to know them well enough to know "OK, I know I this will simplify if I use a factor formula", or "OK, I know if I can manipulate this into sec x + sec^2 x then those are both things I can integrate using the formula book".
You don't get "deep" understanding of maths topics unless you use them a lot. For a lot of people (it was true for me), C3 and C4 are the first places this really starts biting you. It doesn't take great understanding to be able to get through A-level questions, but it takes a lot more work to be able to use the techniques as needed in other questions. This doesn't mean "Oh, no, I'm doomed at STEP!". But it probably does mean you'll start realising "Damn, I really need to practice these topics".
OK, so this is just my personal opinion, but I'm going to be honest: I think the previous degree is a big issue. I obviously don't have the experience with 100s of students that admissions tutors have, but I think you have to "thread a pretty fine needle" between "He's already done a degree and he didn't do very well" and "He's already done a degree and done well so it would be a waste for him to go back to the start of another undergrad degree". (It would also depend what the previous degree was).
For maths, I don't think the GCSEs and previous A-levels are necessarily that big an issue, but the overall amount of time you've had that could reasonably be considered "studying towards A-levels" definitely is. (in other words, if you've spent 2 years doing A-levels, 3 years doing a maths-related degree, and then spent another year retaking the A-levels, then you've basically taken 6 years to get to the same point most applicants will have managed in 2 years. Since most people find the workload at Cambridge a big shock after A-levels, I think there's no escaping that this will cause a lot of concern.
On a similar note, if I'm going to be honest, if you're having to "work your ass off" for the A-levels, that's not a terribly good sign. STEP is a lot more work than A-levels. Not like 50% more, it's several times more work, IMHO.
That said, I've got no idea how to estimate a probability for this. Do you have an offer or are you planning on applying next year? In the latter case I would absolutely be sounding out colleges now on how they feel about your circumstances.