Actually it looks like this is a standard part of the John Lewis policy.
You need receipts or valuations (which I'm pretty sure I have but need to check). Not entirely sure how that works with something that's potentially appreciated, guess I'd need a valuation in that case.
A lot of policies have them defined as "valuable items" or similar (basically small, expensive stuff it seems).
My insurance has a total of £20k of valuable items with an individual limit of £3k and it didn't cost much extra. Ten or twenty quid maybe.
Items under £3k don't need to be individually listed.