Cambridge has no requirement as to the number of A/A* in GCSE as long as at least 6 GCSEs have been done
Most universities will demand at least AAABB or above in Biology (or Human Biology), Chemistry, English Language, Mathematics, and Physics.
Oxford is very demanding on GCSE's and the average applicant there has 9.8 A* (dependant on you cohort as a school)
In general a medicine applicant is expected to excel in academics, as this is the minimum requirement (given that work experience and reflexion on a career on medicine is the real divider among students)
What you need to focus most on are very (VERY) strong science A levels. Chemistry is compulsory, and doing Maths, Bio and Physics is advisable. You should consider taking 3 science A levels, as 98% of applicants do (and 3/4 science A levels has the highest rate of successful entry)
Doing the 4 sciences for A level is not necessary, and indeed it may impair your ability to deal with work experience and extra-curricular research. That being said, doing the 4 sciences will be very beneficial when it comes to preparing for BMAT (which is indeed one of the main requirements for Cambridge)
Edit: Psychology is not considered a relevant subject for medicine, so you would probably be better off not choosing it if you really don't think you can choose maths instead of it.