Irish student applying to UK university.

I have a cousin who lives in Ireland; he got his A-Level results yesterday:

English Language: A
French: B
Irish: B
History: B
Economics: C

I think he's only applied to Irish universities. He wants to do a Law course. I haven't heard much from him (as I'm abroad at the moment), so I don't know what his current plans are.
My question is...would it be possible for him to apply to a uni in the UK this year? Last year, he got an offer from Queen Mary's, but he didn't meet their offer. He retook his exams, and I think he got better grades this year. However, I don't think he applied to any UK universities this year. Is there the slightest chance of him getting a placement this year, if he contacted Queen Mary's (or any other uni...)?

I'm going into year 12 next year (I am currently awaiting my GCSE results!), so I don't know much about applying to unis and stuff. I'm just trying to be helpful! :')