Agree with the above post. If it's the social aspect you're looking at, Bath is 100% the way forward. Small city, great facilities and student feel. UCL will house you anywhere around london and it is bloody expensive. Also, academically, Bath and UCL are almost indistinguishable. Conclusion: Bath.
Btw i've lived in london all of my life and specifically chose to go to a uni outside of it. Bath so happens to be my no.1 choice :-).