Really depends on a range of factors but pastoral care is very much a part of the package for any university these days (or should be). Usually, it will include a personal tutor, someone who is involved with additional needs and year tutors--all of this is within the department.
Within the university as a whole there should be an educational support unit for additional needs, sometimes a health centre, counselling and various workshops, supports for exam stress, anxiety and so on.
Bath is supposed to be the place for additional needs.
It is also going to depend in part on personalities (whether you gel with your personal tutor--if not, ask for another), whether the department and university really embraces an ethos is which the pastoral matters beyond ticking boxes.
You will probably need to think about staff-student ratios and the course numbers in general because, with the best will, this is going to have an effect.
Peer support or buddy/mentor schemes are a good sign that pastoral care matters and that the department is aware of issues around transition from school to university.
If a student has specific issues, disability, additional needs, mental heath difficulties it is well worth contacting the university in advance and asking specific questions: you can tell a lot by how they respond to this kind of approach.