Have a look on the University of Bath site because there is loads of information on there about accommodation costs and living costs in Bath. There is also a lot of information about what is available in the City.
DD considered Bath and Lancaster and loved both campuses. Bath wanted higher grades though - in the end Bath was first choice because she felt she liked the City better than Lancaster and it was also easier to get to London, Birmingham and Southampton for flights.
Lancaster offers accommodation throughout your course I believe, whereas in Bath you have to move out into a house/flat.
You really need to have a good look around the sites - don't focus on prestige - focus on course content and select on that basis.