st andrews has a great international reputation too - you can regard them as equivalent in the sense of how good they are academically.
with these two specifically, you have to choose based on course structure because theyre so different.
kcl is in England, so follows the English course structure. it is 3 years of uni, with three terms per year. the first year will generally have no flexibility (you will be told exactly what modules to study), the second year will have a little more flexibility, and third year may only have 2 required modules and the rest will be up to you. you will have exams at the end of first year which determine whether you can stay on the course (generally low requirements to pass at this point, theyre just making sure you're not wasting your education so dont stress about them) but your degree will be formed 100% out of third year exams on 2nd and 3rd year modules.
ive not personally looked at kcl or English, so this is just the general British uni course structure and you may want to check for specifics
st andrews is in Scotland so follows scottish course structure. it is four years at uni (which may be worth considering if you're paying 22000 a year or whatever the international fee is). the first two year years are very flexible and you can take up to 3+ subjects, slowly narrowing down to a final 3, 2 or 1 subject(s) which makes up your degree. there are two terms per year, and it is modular. that means that you choose your modules at the start of the each term (there are only 1-2 required modules per subject in year 1 and 2, other modules can come from your own subject or from any subject excluding medicine) and then you sit an exam in each module at the end of that term. there are no end of year exams. this means that over the Christmas holidays, you have an entire month off where you dont need to revise for exams because you already sat your module exams before you finished, and you have not started your next modules. obviously prep is useful, but you dont go back to those modules you've already done. your degree is made up of your scores in the module exams over years 3 and 4.
i love the Scottish course structure because it seems much less stressful than here in England, but its completely personal preference and i think that's the biggest difference between those two unis