Glasgow, Edinburgh and Royal Holloway are all far far far better unis than any of the others you mentioned (with the except of maybe City uni and Queen Mary's). Please do yourself some justice and apply to some better unis! If you're looking at those 3 I've mentioned, you want to be setting your sights a lot higher than the other unis you've mentioned which are all really crap for psychology.
Try Sussex, Surrey, Nottingham, Manchester, UEA, Kent, Leeds, Newcastle if you're looking for great unis and pretty decent psychology departments on par with Glasgow/Edinburgh/RH.