It depends entirely on the specific course at the specific college- you have to do the research.
You can come to Classics with no Latin. For Oxford, you would have to sit the CLAT (Classics Language Aptitude Test). You can check out past papers online to see if the exam will suit you. For KCL if you want to do Latin, it is hard to do that w/o AP Latin- but you can do Classical Studies w/o Latin.
The thing is, in the UK you go straight into your subject. Each university will tell you how much background they expect you to have. If you are a true Classics student shooting for the top (Oxbridge) even without it being available in your school, you have probably already taught yourself some Latin and Greek because you totally nerd out about Classics- and if you don’t, Oxbridge isn’t for you.