As a Manchester Uni Graduate (UMIST) I would have to say look carefully into all the different courses being offered by the uni in the comp sci department I know that
there is a course that includes an HCI module in it but I've not managed to find it yet. (as I remember it was an optional module) They also have a Comp Sci and Maths joint honours degree. This may also suit you, dependent upon what you are looking for
in a course.
I wouldn't rush the decision of which of the courses to take. Make sure it's the right one from the start. It is possible to switch from one course to another in the first year so long as there is space on the one you want to move to. (this however is subject
to the universities discression)
When I was there the department did a Computation course which had a good mixture of all the things you are looking for, it may be worth finding it's current equivalent.
Also something to be aware of is the fact that at Manchester they currently have the Computer Science department and the Informatics department. Informatics is due to be split up into the Computer Science department and the School of Management. The
Centre for HCI is based in the
Informatics department currently and you may also wish to look at the courses in that department, however with all the changes to the department you may find that there is a lot of unknowns around the futures
of those courses. It would be worth getting in touch with the department and finding out which of those courses is likely to stick around if you want to concentrate more on HCI than Mathematics.
Best of luck with your application. You'll enjoy Manchester, it's a fun city and one I always enjoy going back to!