Latin, Greek or German?

Latin is an academically rigorous subject blah blah blah blah. The usual spiel. Take German. Yes, Latin is all well and good but you're not overly likely to start needing to pick up dozens of languages. German at least might have some direct application.

Thanks? What about Greek though? Greek might have some direct application too.

Not really, no. I'm a Classicist specialising in early Greek stuff and, honestly, it has very little application to anything really. Latin is useful in the sense that, beyond the usual stuff about the mental exercise of its grammar and its contribution to English vocabulary, it serves as a wonderful bridge to medieval and renaissance traditions of thought. Plus the link to modern European languages.

Greek can't boast of any that. German of course directly puts a modern European language in your hands. It depends on what you want to go for really.

I want to study law at Cambridge or LSE. So far I have chosen maths, history and English Literature. Which one of Latin, Greek and German will be the most useful?

Definitely German. There are far more resources available for German and it has more real-life uses. The Wort für Wort vocab book (£6) is a must if you're doing it to A-level.