Many universities that don't sound like former polytechnics make the list:
http://www.bps.org.uk/bpslegacy/acTry here. You need the chartered membership in order to apply for the professional doctorates and all of these give you that. Masters are generally looked upon more highly by other employers but for further training in psychology it doesn't much matter as long as it's accredited.
It is worth taking a look at the course itself and checking what the components of the course are. A lot of people on my conversion psychology course applied for the prestige of the university and there's already been a massive dropout rate. A number of people have been complaining that the course wasn't what they expected as well and in fairness to the course tutors, that's the students' fault, not theirs.
I'd say it probably isn't worth doing a massive relocation for the conversion course if your local university does it and you're doing it for the accreditation, not just the subject. Your CV will count more than anything else when it comes to the further professional development you're looking for, and hopefully your education will make up the smallest section by that stage. I went to a university that was fairly local to me and yes I did pick the most prestigious course to apply to. However, it also happened to be a specialist course and closely related to the career I hope to pursue.
If you're interested in pursuing professional doctorates in psychology, it's worth checking if the university you apply to also offers those programmes or has any links to universities that do. It's a good way to get under the radar so to speak. Northumbria for instance has a lot of links with Newcastle's Clinical and Educational Psychology Professional Doctorates, so their conversion has an advantage over say Teeside for those departments. However, Teeside runs a counselling psychology doctorate, so that has a good link to that if it's something you're interested in.
Be careful with some of the courses though. Some require you have a certain number of credits in psychology before starting and it's actually not something they always check. Conversion and Masters students are annual herds of cash cows as far as many of the universities are concerned so you need to be careful.
As someone who's doing a Masters however, as opposed to a graduate conversion diploma, a few words of warning for you. At Masters level conversion you are expected to work at a graduate level. They're tough. I don't know what the standard is at the graduate diploma level, but the fact you're getting a Masters is not just a grander title. It's a higher standard of work than you'll have previously done and you will work for it. It's damn difficult to get a merit or a distinction at this level and you're going to want to come out with one of those. So many people on my course expected to find it easy and now they're thinking they'll be happy just to pass. There are a number of psychology graduates on my course (don't entirely know why) and they struggle with the standard expected of them. One of the dropouts this year was a psychology graduate from overseas. She failed her first assignment and realised it could do her more damage than good to keep going.
It's worth doing, but you need to know you can do it well. From what I can tell, the Masters level is tougher than diploma, although you get the same accredited status with either one. The standard expected of you at Masters level, though, is higher. Don't be swayed by the prestige of a Masters. You need to be ready for it. The better your first degree, the more academic the subject was, the easier you'll find it.
Consider why you're doing it as well. You won't qualify your way into any job armed just with a conversion course, particularly a psychology trainee position. You need a good CV. Consider going part time with a course if you can. You'll lose a year of your working life doing a conversion course and that's telling when you come to building up your experience. Factor that into your decision making too.
Sorry to be hard-faced. I just never imagined how tough the subject would be. You have to have a certain amount of blind confidence in yourself in order to choose to do it in the first place and then some more to keep going once you're there. These conversion programmes have a high drop out rate though and you need to know that it's not inconceivable that you may become a member of that statistical group. It's a lot of money and a lot of time you won't get back if it all goes wrong. That's what I think of when I think of the dropouts. Some of them clearly weren't right for the course to begin with. These are some of the things they should have been thinking about when they signed up.