Another teacher here. In my long experience, schools are really not the ones telling people that D of E, music grades, tiddlywinks etc matter to high grade tariff universities' admissions teams. At least no-one who knows anything about UCAS would say that. The most clunkingly awful personal statements I see are almost always ghost-written by dad, or less often, mum, under that misapprehension.
D of E, playing in teams etc are wonderful on their own terms, and certainly educational in the broadest, best sense, but they are not an artificial shoe-horn to funnell middle-class kids to uni.
If applicants do mention extra/co curricular activities on a personal statement, they should use them to continue to demonstrate how they are suitable for THIS course not just a random, 'and I play in an orchestra' or whatever. My advice is to make the whole statement at least 80% academic and entirely focused on the subject applied for. You can bring in any life experience to do this, so If applying for Sports Science or Music, then games/violin will be relevant, but you still need to explain why. If you wanted to do Physics, say and are also a keen mountain biker, you could show off knowledge of the mechanics of a bike, say, when writing about the hobby.
What unis do like is evidence of supra-curricular learning, ie going beyond the syllabus academically. They will quite reasonably expect kids from more privileged backgrounds to show more academic independence than others.
Listen to podcasts, eg from radio 4, READ, do an EPQ, take free MOOCS, do relevant work experience if possible, especially for medics, dentists, vets (to show people skills, so not necessarily in a medical etc setting). Above all, apply for a subject you genuinely love and do enough work in advance to find out why you love it so much. Then explain that.