BA and BSc psych have very little difference, if any!!
Seriously, at Bangor you can apply for BSc or BA... and we all have the same lectures, do the same modules, get the choice of the same modules.
Many unis will take you on with out anything sciencey. There are normally a few GCSE grades you need such as maths but thats it.
Im going Psychology BSc and my A level were Psych, Bio, English lit (and critical thinking). I got offers from all my 5 unis with this subjects, all Psychology BScs and my unis included places like Warwick.
You can get on a course with one science. But since you're doing biology and psychology that counts as two sciences, which is fine. I suppose the best way is to ask them, but some unis say they have no preference at all on the subjects.The only thing is though that if you take a BA over a BSc becoming a psychologist could possibly be longer because you may need to do a conversion course. But if you aren't aiming to be a psychologist then it doesn't matter.
I remember looking at the St. Andrews courses. They psychology stuff you did were the same, but other subjects you did in the first year or two depending on if you were MA or BSc.
Plus, i think you would be suprised how far the bio and psych will get you.