It can make quiet a big difference. Most psychology departments are pretty balanced, but others specialise into different areas. Newcastle, for example, have a tiny psychology department but mostly people from their neuroscience institute lecture in the course. Others may focus on social psychology and may be nested within a politics/social science department.
The basic BPS core courses are not very big (my uni did all the core modules in one year), so you may be disapointed if you don't double check what modules are available.
In addition, if you want to get into certain fields (e.g. clinical psychology), its great to also do your degree in somewhere which does clinical psychology research, especially if you can do your dissertation on it. Making contacts via dissertation supervisors is amazingly useful. But this is thinking far too in advance for most people!