You can get in Leicester, which has a research quality rating in Psychology of 83% (joint 25th in the UK), according to The Complete University Guide. This is equal with Reading, and higher than Nottingham (82%), Queen Mary University of London (82%), Leeds (82%), Durham (81%), Newcastle (80%), Bath (76%), and many others.
Royal Holloway has a research rating of 87% for it (joint 12th in the UK, with Stratchclyde, Birmingham, and Liverpool). As well as all of the universities mentioned in the first paragraph, this is higher than Sheffield, Exeter, St Andrews (all 86%), Manchester (85%), Warwick (84%), and others.
I can't see what the GCSE requirements are for Nottingham, so you may be able to get in there too. You can get in Queen Mary University of London, Strathclyde, St Andrews, and Warwick.
If you're eligible for contextual offers, that may benefit you in some cases for these and other universities.