What to do with a 2:2?
Admissions tutors will not normally accept graduates with a 2:2 unless they have achieved some higher qualification too.
Any psychology Masters degree would be relevant: the main thing is that the MSc demonstrates applied research ability
A taught MSc would be less relevant unless there is a heavy emphasis on research methods.
Courses are looking for evidence that the person has the required academic and research ability.
Usually this means an MSc or MPhil in which the candidate has successfully completed an applied research project.
Contact the universities directly for more specific information on their entry criteria.
What funding is available?
Course organisers are usually best placed to give advice on funding. There are a number of websites that offer information about postgraduate funding.
A few examples are listed overleaf: