With an under-grad degree, if you are going into some sort of graduate employment scheme, the prestige of the university has an impact from people who hire I've spoken to.
If you're doing an ology, and planning to go into the public sector in some way, no, it doesn't (again from speaking with recruiters)
If you're Oxbridge, not going down the "Oxbridge track", I think it can sometimes work against you, in that people think you're too privileged/stuck up/whatever and discriminate against you.
When it comes to MA study, the course itself is more important - and how it's valued in the field you want to go in to: which often doesn't correspond much/at all even with university rankings.
I couldn't do my job now (academia) without my degrees - but it's the one question that has never come up when we recruit people: we're not interested where they graduated from, or even what their grades were (we just care how many books they have eligible for the next cycle of research funding 
)
The job I did before, I also needed my degrees for, and wouldn't have been eligible without them: but no-one cared where they were from.
I think it depends what you are doing, and what you aspire to do, in all honesty.
And it's very, very difficult to get any kind of decent-ish job (by which I mean office-type professional-type job) without a degree: possible - but very hard, as the "degree" is the tickbox by which they whittle down numbers.