Part of me says yes, part of me says no.
I do think there's more to it than what university you go to as to whether you get the job or not. I think experience is also important (more so these days when it seems pretty much everyone has a degree) and the people themselves and how they come across and how they will fit into the team, etc. However I can't help thinking if there was no difference between two candidates other than one went to a good Russell Group university and the other went to a bottom of the league table ex-poly then it might become important iyswim?
Also I'm not an employer but I can't help thinking that because so many people these days go to university that employers do have to differentiate between candidates somehow to choose who to invite in for an interview and one of the easiest ways to do that would be by what university they went to. I actually know someone who does interview for graduate jobs and to narrow applications down he immediately disregards any that went to universities that he hasn't heard of and then works from there.
The whole university snobbery thing seems to be worse on the internet.