Your question is pretty unspecific and I'm no expert, so it's very hard to give an answer beyond 'yes, but maybe not that much'.
What I do know is this: universities do make some effort to make their assessment standards resemble each other, and while a First from Prestigious Institution X might be more impressive, the people assessing postgrad applications know that you don't normally get a First at a respectable but unspectacular university without effort and thought.
They may also be prepared to make allowances for factors that might make getting a First harder, at least in some respects, at a less prestigious uni -- fewer competitive peers whose presence might spur you on, less access to resources, less pastoral support &c.
Finally, because they work within your discipline they are more likely to be alert to particular departmental strengths or significant academics at your undergraduate department -- the man or woman on the Clapham omnibus might find an elite university name impressive, but the people assessing postgrad applications will have a more nuanced picture.
If you're doing well as an undergraduate and your areas of interest for further study match other unis' strengths, I'd say you should totally consider applying to them even if they're seemingly more prestigious. Though as I said, I'm no expert. If you haven't already, do canvass opinion from the people teaching you. It's difficult to get impartial advice, but even partial advice can be pretty helpful (revealing, even).