Generally they're just fulfilling their remit to ensure the parent's thought about it and not just removed the child from school to solve a school issue and doing nothing.
Don't be unnerved by the word 'evidence' a letter is evidence.
You don't have to do any proving of anything unless they suggest you aren't making provision, and some will feel you shouldn't entertain the request, but if you want to, the way to satisfy them in your situation, is send an 'plan,' of what your provision will be in letter form.
Stating (should you choose) that you've chosen to take a break for the transition from one kind of education to another, (add blurb about learning to self motivate rather than only showing up to be spoon fed/receive provision if you choose) and Christmas holidays, so it is early days in terms of shaping final provision, but: DD is currently engaged in whatever the four classes are, the sport, and music, and will be starting Y subjects (the 3 Igcse's) in 2nd (or whichever) week of Jan.
Then add whatever less/un structured provision you have going on, ie; organisational skills, researching college, life skills (cooking, banking etc) anime, ict art, film appreciation, or whatever else you/she does as part and parcel of unstructured education.
Add: provision may be subject to change in order to meet any changing or additional needs if or when they arise, in your own words.
If you want to chuck in a basic ed philosophy (children learn best when self motivated, tailored to their needs, etc, or whatever you believe) and a list of all the resources you know exist as 'a selection of possible resources available', you'll knock their tick boxes socks off.
Hth