It sometimes matters, it sometimes doesn't. It depends which uni you're talking, the grade you get, what you're studying, and the job you want to go for. Often, more prestigious unis will have better job prospects because the deliverance of the course is better IMO. I have a psych degree from a "lesser" uni and know someone who went to Cambridge, and although our courses gave us exactly the same basis for graduate entry to the BPS, the things they studied were amazing, the labs, the social experiments, and the contacts that the unis brought it. Contacts and experience can get you roles, and if you're proactive you can get these no matter which uni you go to. I'm not saying it's the be all and end all for every subject, but it's just an example of one of many factors that you may not have thought about. I think "better" unis are a better platform, and make it easier to flourish, but that's not to say that a) it doesn't still take a huge amount of work and b) that you can't do that at a lesser uni, but under your own motivation.