The admissions staff expect everyone to sit the MAT unless they are literally unable to sit it (perhaps due to the country they are in, or due to illness maybe?). Having said that, I suspect they would still consider your application if you didn't sit MAT, and if you are a strong applicant they may give you an offer (which would almost certainly include STEP). However, I think it is fair to say you wouldn't be doing yourself any favours by not sitting the MAT.
(Note: this advice is partly guesswork and partly based on what the staff said when I went to the Open Day last year and asked for clarification on this very topic).
Personally, I recommend you sit the MAT. If you take MAT and do sufficiently well (whatever that means), you can get an offer of A*A*A with no STEP. Most of the top unis nowadays are handing out very similar offers of something like A*A*A + 2 in STEP or A*AA + 1 in STEP. Having a non-STEP offer gives you some nice options:
a) you can go for a more ambitious firm choice if you want to, knowing your backup choice (Imperial) is relatively safe;
b) you can put Imperial as your firm choice, allowing you to practice STEP at your leisure and just enjoy preparing for the exam (if, at this point, you decide to sit it at all).
A lot of people will have virtually identical firm and insurance offers which include STEP, meaning their insurance is basically pointless and if they have a bad day in STEP they may not have a place at uni at all.
FYI: I took the MAT, put Cambridge as firm and Imperial as insurance (with an A*A*A offer), and am now going to Imperial.
Hope this helps.