OP, just another thing to mention. My niece applied to Cambridge in this last cycle. Not for MML, but for English Lit (slightly more competitive than MML but not drastically so, in terms of the offer rates).
She was at a leading London Day School (independent). Her GCSEs were all 9s, except for Maths (7) and Physics (7). But she had 9s in English Lit, English Lang, Drama, French, Spanish, History, Religion and Philosiphy - all of which are in the 'preferred subjects list' for English Lit, so she thought she'd give it a go. She also had 9s in Biology and Chemistry.
She did the English admissions test set by the college she applied to. Had interviews. Did not get in. She requested feedback which basically stated that her interview scores had been very strong, as had the admissions test results and the two essays she had had to send in. But the reason she didn't get in was the GCSE grade 7s - in Maths and Physics (!) - because these are low for her school. At the time if applying, my niece already had an A star EPQ and was predicted all A-stars in English, History, Drama snd Philosophy at A-level, but no - it was the 7s in Maths and Physics that were the issue - apparently! I think it's because they have so many applying with straight 9s, they have to decide somehow.
But anyway, she's off elsewhere and will do brilliantly there.