It depends on which hospital you're based in but pretty much all of them do have areas for students. They vary in what sorts of facilities are there, though.
Charing Cross has the Reynolds bar which has a bar (obviously
), a gym, library, computer room etc. There's also a swimming pool and sports hall in the hospital. Same in Hammersmith Hospital minus the bar. St Mary's has a lot of stuff as well but there's a lot of drama happening there so I don't know what will happen.
Chelsea and Westminster also have a student common room, lecture theatre and library. There's also a cinema there for patients (sometimes if you're lucky you can use it and it has latest movies currently in real cinemas iirc, and they sometimes put a lectures there) and live music playing, but that's for the general public.
Northwick Park, Hillingdon and Ealing have areas libraries and study areas for students. St Peter's has a postgraduate education centre which is shared by doctors and medical students, but they also have a separate medical student common room as well (which is shared by St George's as well).
There are some places like the Royal Brompton which don't have any areas for medical students though. But they are super specialised and hardly have students there unless you choose to do a student selected placement there. It's OK for Brompton though, as it's about 10 minutes away from the South Ken campus so you can go there or just hang out in the doctors offices/staff rooms.
That's all off the top of my head. Charing Cross, Hammersmith and St Mary's have larger areas for students. Most of the others also have decent areas though.