Just a few other points in relation to the OP, usually cambridge says they like all a levels done together, so having a maths a level in the bag at the end of y12 isnt necessarily a positive. They recognise that some schools do it this way, so its not necessarily a negative either. It is what it is.
For supercurriculars, as well as the cam ones, there are list(s) at oxford
https://www.st-annes.ox.ac.uk/study-here/undergraduate/outreach/students/super-curriculars-and-resources/and the livestream/maths club talks and ... Its less about summer schools/programs, more about what youve done yourself (books, projects, ...) So focus on what youre doing yourself (not being taught or shadowing students, whatever that is) and anything in addition is a bonus. In the personal statement / interview, they really want to see two things, 1) that youre capable of passing step 2) that youre capable of learning in the tutorial system. The latter is where its important to demonstrate what you did yourself, how you learnt it.
Theyre not necessarily that related, but Im surprised if youre confident of getting 1,1 in step but are getting bronze in smc which is ~6+/25 questions right. Arguably the ukmt stuff is more related to the interview, so talking about elementary maths/how to solve problems/ideas/.... So if youre interested in maths, why didnt you put a bit of effort into preparing for the challenges / problem solving etc? If youve done other maths stuff and are not interested in the ukmt stuff, fair enough, but one recommended booklet for preparing for the interview is bowlers, and that has a reasonable ukmt challenge/olympiad slant, for want of a better term.
For the colleges, trinity is more competitive than the others, but not stupidly so and you end up with the same degree at the end, having done the same course. But youd prepare the same over the next 7 months for whichever one you apply to, so it really would be last of the things to worry about.