Students often drift into studying maths at university, with very little understanding of what maths actually is (particularly since A levels are so low level at the moment). Students who apply for physics, engineering, computer science have all made more "conscious" choices and tend to have more interest and passion for their subjects. Students apply for maths thinking that it keeps their options open and is well-respected by employers; they also hope it will be as easy as at school.
Any student with As and A*s will be able to get offers from many good universities for maths but this won't be enough for Oxbridge: MAT and STEP together with the interviews filter out those who genuinely have talent for the subject.
I suspect this year's numbers are anomalous but they are still surprising: such a low success rate wouldn't be expected from Westminster because they are usually able to judge who are serious Oxbridge candidates. In general a lot of the students who apply for maths at Oxbridge are well below the cut, even though they have A*s predicted, but top schools generally don't put forward weaker students. (Schools who don't often send students to Oxbridge do, because they can't judge how good their candidates actually are.)
BTW I don't think any school in the UK is preparing students better for maths at university than Westminster - Westminster is quite successful in Olympiads and sends a fair few to Trinity camps etc. Moreover, preparation and training beyond MAT and STEP practise is not necessary and does not really confer any advantage. Teaching ahead, i.e. covering first year university material, will not give an advantage in an Oxbridge interview as it is obvious that the candidate has met the material before, so the interviewer just switches topic to something they haven't met, sees how the student responds.