Maybe OP just had a really well written personal statement with mature student printed at the top like mine?
I'm in a similar boat (although not as prestigious as Cambridge), been accepted into a C Math, C English GCSE, B B B A-level course.
My GCSE's were B in Math, D in English, D in English Literature, D in Double Science, E's in everything else and have never taken my A-levels, instead I'm turning 31 years old and just finished my first year with The Open University using this as replacement of A-levels.
The grades are generally for people under the age of 20,
Edit: I'd also like to add that if I had taken the optional more advanced math module last year, the University of Sheffield said they would of taken me (AAA GCSE, AAB A-levels req) when I rang them up during clearing, my first round of applications was for year 2 entry but what I learnt just wasn't transferable for a comp sci degree.