Birmingham has 4 - BCU, Aston, Uni of Birmingham and university college Birmingham. I don't know about university college Birmingham but BCU Aston and Uni of Bham all have campuses pretty close together.
Liverpool has at least 3 (Liverpool, Liverpool John Moores, Liverpool Hope), Birmingham has at least 3 (Birmingham, Aston, Birmingham City) and London has about 19 I think.
Edit; London has loads really
Most people say here that Birmingham has 3/4 Universities, technically that's correct if you're following along lines of Birmingham which are quite small and most people travel across these lines like there's no lines everyday. However, if you follow West Midlands county which are pretty much limit for most people living in West Midlands due to transport differences between outside and inside county.
There are 7/6 universities in west Midlands county.