Hi!
I am current third-year student at Lancaster University. The most important factor in the decision to me was going to open days. Lancaster was the only university open day that I went to that I could picture myself studying at for three years, and I think this is a really important factor in choosing your uni.
If you like the campuses equally, then another factor is what the courses consist of - as a maths student, do you like statistics? Does one uni do more stats than the other? If you look at the course content there will most likely be one which fits better with your tastes, I had a friend that went to Warwick for maths, and I know that the modules were really important to him as although he loved maths, he didn't love all aspects of maths and Warwick allowed him to choose the modules he wanted to do.
Another important factor is the cities themselves: although Birmingham and Sheffield probably aren't drastically different, is there something that it is important for you to have access to? Maybe one university has a better sports centre, or societies you want to join, and the other doesn't.
Hope this helps!
~ Georgia