IB student applying for psychology without biology

Hi guys!

I'm in year 11, choosing my subjects. I really want to study psychology, and I've looked at a lot of courses (Psychological and Behavioural Sciences at Cambridge (v v long shot, but still), Natural Sciences at Durham, Cognitive Science at Edinburgh, Psychology BSc at Bristol). All of them specify really high grades, which I'm two years away from properly worrying about yet. Some of them want two sciences at HL; Cambridge wants HL Mathematics. I want to study:

Maths HL
Physics HL
History HL
English Lit SL
Spanish B SL
Economics SL

(I know how hard HL Maths is; I love Maths, and I'm prepared for it.) I don't want to do Biology HL, because my school's option topic is ecology, and OH MY GOD NEVER AGAIN. I don't want to do Biology SL, either, because Biology SL is what everyone who does IB and hates science does, and I don't want to be in a class where no one really wants to be there. Also, unis don't care about SLs, and if that's the case I really want to study Economics.

Sorry for the long post. Do you think I could be accepted for these courses without Biology, or would maths and physics show enough understanding of the scientific method?

Thanks!
Rx