I misread your post. You are asking about about biomedical science rather than biomedical engineering. Still the latter is also worth look at as there are quite a lot of options with a biochemistry focus.
DD has an intercalated degree from Imperial in Bio-medical engineering, and opted mainly for bio mechanics.
She too was torn between medicine and engineering, but in the end decided this combination allowed for both. Her Imperial tutor has said that if she wants to continue with Engineering she can go straight onto the Masters course. She did her two month elective in an Imperial research lab and they have said to let them know if she wants to go onto a PhD.
Like your son she spent time working in a care home. Unlike your son she loved it and even when back to have lunch with her favourite old ladies. The manager suggested she thought that it was important for prospective medics to do this. Some people find it difficult to work with the elderly. It is better to find this out early.
DD did not have FM and effectively landed into the third year of the engineering degree with only a three week pre-sessional catch up maths course, and survived. She had an A* in maths and my guess is that almost all courses in Imperial will be quite mathematical, and that it would be important to have sufficient aptitude to be able to do well in FM if you had taken it. Some of her peers, despite top grades in everything, struggled.
I don't know anything about the Cambridge course, but DD loved Imperial. Fellow students were very focussed, and she was able to find a good group of work-hard play hard, sporty types. There is a lot of research going on, which teaching staff are engaged in, and there is a real sense of things happening. All the courses she took were open to Masters students from all over the place, and the teaching/assessment had a large element of project work. Frustrating at first, but the ability to work in multi cultural multi disciplinary groups is a really useful skill to gain.
I am not sure about extra curricular. Sheer academic horsepower seems to be the main way in, though DD took electronics and physics at A level so could also demonstrate interest.