I'd never dream of travelling uninsured, and with the amount I do an annual policy is pretty good value all round. I've been with Boots for several years.
I've fortunately only had to make one claim. Between us, my partner and I managed to leave some Bose headphones (not cheap) in a hotel, with a CD player and a CD in the side pocket of the case. The CD was one of a set of 3 (an opera). All, you might have thought, highly dodgy stuff, particularly as I didn't discover it for several days, and was already at sea on a cruise ship.
They paid the claim, no trouble, no hassle. It included the full cost of a replacement set of CDs, on condition that I sent them the remains of the set from which that single disc was lost.