Beckandcall, agree. Colleges vary, but all Cambridge science students have to do a maths course in 1st year. It's no good sticking heads in the sand and hoping for the best. If OP is keen on oxbridge (no sign of that - just mumsnet hype I think) then she/he needs to check colleges. Yes, everyone applies for nat sci.
Notcitrus, you're not the first I've heard of to get in with no maths (maybe you're her though!) but was it not just a tad daunting to be the one with (substantially) least maths and physics? Be honest, for the benefit of those taking advice from here. Getting into somewhere is just the start. Two of my DCs went with gaps that most of their peers didn't have and it was undoubtedly harder for both, at least in 1st year, because of it. (Of course, the gaps meant they had something the others didn't, but that was rather less helpful at the time! 'Preferred' subjects are stated for a reason)
OP: you seem to be in a difficult position. You said you can no longer do Eng Lang? You seem not keen on all sciences/maths, but still want to do neurobiology from biology and chemistry A levels - and probably Psychology as the third. I would stick to your guns over a fourth and pick from the remaining block what best suits your interest as well as aptitude - so perhaps not Physics from what you say! That is, so long as you're realistic about where you can apply with these A levels and your likely grades. You'll be doing what ASs were meant to do and keeping your education broad. But before you finalise, get your school's advice, check university requirements, and email some admissions officers as suggested. Ask for the A level profile of people on the courses. You only have 5 choices for university, so you don't need to meet everyone's requirements. [Hobbyhorse warning] It's a real shame if university science students are bludgeoned into doing all sciences from age 16. No wonder they get treated as geeks and weirdos by arts students.
To play my own devil's advocate though, the point I'd make about maths is that you do need it as a scientist, you can't afford to be afraid of it. A level would allow you to continue to study it, and you'd come out more confident and competent even if you don't get a great grade and can't cope with some of it - it's easy to lose sight of the value of A level courses: two more years of study, they aren't just about the grade. But don't do maths if the thought makes your heart sink. Do, though, get some maths practice before you head off to university. (Coincidentally or not, I think Cambridge tell their scientists to practise their maths in the summer before they arrive!)