There are several olympiads that UKMT opens. You will first have to try the IMC (intermediate competition). If you get some points above the requirement you will be invited to the olympiad. (this will depend on your age/year group). Another olympiad will be the BMO (British Mathematical Olympiad) round 1. You can either meet the requirement of the SMC (senior competition) or just apply for the olympiad. If you are successful you will be invited to the next round which is BMO round 2.
Some other olympiads you may consider is BPhO (British Physics Olympiad), UKChO (UK Chemistry Olympiad) or BBO (British Biology Olympiad). Just type those name in google and you'll figure out how to apply for those. There are something for astrophysics as well which I cannot remember at the moment. Most of the olympiads I think it is school based which means that the school should pay the institutes to take the olympiads. First ask your maths/science teachers about it and gain more information from them.
Don't forget that having lots of super curricular with olympiads and listing them out doesn't ensure your place in top universities like Cambridge. You'll have to link it with the major you want to study and how those experiences of olympiads helped you to pursue your choice and how they shaped you as a person who is suitable for the major.
Good luck with Cambridge!