As someone who spent a long time in various positions relating to hiring and placing staff, I'm pretty sure that 95% of employers don't care about university rankings. The 5% tend to be specialist graduate recruiters or academic employers looking for very specific things, or operate a bit of an old boys' network. The rest will probably have heard of Oxbridge plus a handful of universities they've had direct experience of. They have better things to do than worry about whether Bath is ranked above Bristol. Even proper 'graduate' schemes seem to take a very relaxed view. My brother got onto a graduate scheme at PWC with a low 2:1 in sociology from Brighton. He qualified as a chartered accountant a couple of years ago and seems to be coping rather well.
I think even those employers who do look at apparent prestige do so with a pinch of salt. There's so much in the relative 'prestige' of an institution that is truly irrelevant to your education, it surprises me how it's even factored in. Research, for example. How does the quality of research carried out at your university really affect the education you receive unless you're a researcher yourself? The fact that my lecturer is doing some very expensive and important research for someone doesn't mean he's any better at explaining basic theory (completely unrelated to his research, which it'd take you 10 years to understand) to undergraduate students. If anything, I tend to find that those academics heavily involved in research are far more interested in research than teaching. Research quality only realistically becomes relevant in 99% of departments during postgraduate study, when you become a researcher yourself.
Entry grades are used for rankings too. Does the fact that an institution requires AAA automatically mean the teaching is better or that students will be better employees? No. Your A levels are a decent basic measure of pre-adulthood intelligence in an academic setting but that's it. You can't define the quality of education at a university based on the grades someone achieved elsewhere. Does a poll of academics' personal preferences (used in most ranking systems) mean anything? Considering that polls of academics have often managed to rank non-existent departments quite highly (for example, Princeton law school achieved a 7th place finish in the mid-2000s, despite Princeton not having a law school), this is probably irrelevant too.
Rankings and 'prestige' perception measures what can be measured, not what is relevant. And the relevant stuff can't be measured.
The overwhelming majority of employers (rightly) employ the candidate, not the institution.