I want to take STEP, but I also need to take the NSAA

As I said in the title (a little wordy, sorry), I really want/need to take STEP, so my application can stand out, and additionally so I can apply for Maths at King’s and Bath whilst applying for Physics at UCL, Imperial and Cambridge. For Physics at Cambridge I will need to take the NSAA exam. Will these two coincide or create any complications? Is this feasible? Thanks!

STEP preparation can be very time-consuming and the "benefit" is arguably negligible if it isn't an actual requirement (Cambridge) or allows you to drop a grade in your A levels (a very small selection of unis). Unless you're sure it's going to benefit your application (i.e. explicitly stated in the entrance requirements) I would be very wary about adding it on to your existing workload.

I see what you mean, my workload at the moment is already quite arduous. I would like to apply to Maths at King’s and Bath, as I said, but of course I can just apply for Physics there too. How long do you think STEP will take?

hard to say as it depends on the candidate! what are the entrance requirements for Kings / Bath, and what grades are you working at?

EDIT: I'd really fix on ONE subject to study if I were you and then focus your application / personal statement on either Maths OR physics