There are no essential subjects needed for a psychology degree except at least one science A-level.
But there are certainly subjects that do help: Maths, Psychology and Biology will all be useful. Other than that you can choose basically anything. I really don't think Oxford/Cambridge/UCL would mind if you chose Further maths over Chemistry/Biology if that's what you want to do. Personally I would do Biology, but again, it's up to you; they're not going to discriminate against any of those subjects over the others.