UKMT competitions are not an uncommon thing for students to try, although by no means necessary. Wider reading around your subject area would be a generally anticipated - I'd suggest over the summer after year 12 looking at some degree level topics in e.g. analysis or abstract linear algebra or something to get an idea of what degree level maths is actually like (very different from A-level - much more abstract, often largely proof based). Otherwise preparing for the MAT if applying to Oxford, or for interview generally and then STEP later for Cambridge.
Note that applying to Oxbridge is not about "standing out". There is no "silver bullet" of something nobody else has done that anyone can tell you that would make them think "oh we must take this student", as firstly if there was such a thing as soon as it was posted online everyone would do it and thus would be a meaningless thing anyway, and secondly that's not how the process works anyway.
Your aim shouldn't be to "stand out" it should be to do what you have to do as well as possible - getting excellent results in your work in A-level and good predicted grades as a result, exploring your broader interests in maths beyond the school curriculum, and trying to apply the maths you have learned to unfamiliar problems (rather than just resigning yourself to learning to the exam). I suspect the students who "stand out" will be standing out for bad reasons, not good ones.