MagicNMedicineIn terms of the admissions process, its difficult to say whether its harder to get in at undergraduate or postgraduate level. At undergraduate level, at the top universities, the numbers are so big that there is much more of a lottery element, which means high quality candidates are more likely to be missed at undergraduate level than they are at postgraduate. It is difficult to discriminate between 18 year olds who have just done A levels or IB so things like GCSEs will come into play which aren't necessarily the best predictor of how good somebody will be on an undergraduate course. For example a bright but not outstanding kid who is organised and motivated, can relentlessly accumulate A*s at GCSE level and have them on their UCAS form, whilst a kid with raw intellectual talent who was a bit distracted during their GCSE years and ended up with more As before getting their finger out at A level, will be behind the game when it comes to applying to the top five unis. Not saying there is anything unfair in that, just it's how bright kids get missed. There are also bright kids who have seemingly ticked all the boxes, who get rejections from top five unis for undergrad, just because of the numbers involved and the fact its a bit of a lottery choosing the best candidates on limited information.
At postgraduate level admissions, it is less of a lottery and more of a meritocracy, because the admissions tutors have got some hard evidence on which to discriminate between candidates - ie university level transcripts which show how a candidate can cope with university level work and what their strengths and weaknesses are. The kid with raw talent who slacked a bit at GCSE and was rejected by the top five for undergrad, but has been focused through uni and has a first class degree, is much more likely to get accepted at postgrad.
The numbers at postgrad are much lower (although overseas students enter the mix more because many who couldn't afford 3 years of international fees can afford 1) and also many of the best undergraduate performers don't bother with postgrad study as they get top jobs straight after finishing uni.
The big barrier for postgraduate study at the top unis is finance, if you are doing a Masters only, which is not attached to a PhD, then in most subjects there is next to no chance of being funded, perhaps in some science subjects there is chance but not the arts, humanities or social sciences. The fees at the top universities are very expensive for Masters, you are looking at five figures for fees and will need to fund your full living costs as their Masters courses are too intense to work part time through them.
As regards prestige, I would regard the prestige of attending a top uni as being equal whether you went to it for undergrad and postgrad and would imagine employers in most fields would feel the same. In academia, you would probably get more prestige for going to a top uni at postgraduate level than undergraduate level (if you want research/academic positions, they kind of ignore your undergraduate study to an extent, its where you went for Masters/PhD that counts more).
One word of warning I would say though, is if you want to work in the City, it might be that a postgrad at a top uni doesn't carry as much weight as an undergrad there would be. I saw this discussed on an investment banking forum once and the general consensus seemed to be that as most of the people working in the City went to top five unis for undergrad, if you get somebody who went to a redbrick and then did a year Masters at LSE etc, it might get their CV through the HR filters rather than being autofiltered out, but they would regard the person as somebody who wasn't good enough at undergrad level but then had money behind them so could afford to fund themselves through a Masters - for sure they'd be respected if they got an MSc from a top institution, but the ones who had done undergrad there might always look slightly down on them.