I've been using the Post Office for a few years now, and every renewal I double check that I'm covered on the bike. It has the usual exclusions of racing etc, but you're OK on your own bike (no size restriction) for touring.
I can't recall what the age limits are, go to their on-line site
here and you can download the actual policy document to check all the small print, as you can on most (all?) insurance sites.
Alternatively if age is the issue, check with Saga (or even Age Concern/Help the Aged I think do some good policies)
I spent some time in Austria and due to food poisoning did need to use their Health Service. I got a bill for the ambulance (£18 which I was more than happy to pay), but the rest of the treatment was covered by the E111 as it was then (EHIC now). If I'd eaten my dinner off the floor in the hospital I wouldn't have got the food poisoning, absolutely spotless and efficient.
My cousin broke his leg in France, and with only the E111 he was expecting a big bill for the "board and lodgings" part of the 7 day stay in hospital while the leg was fixed. He did indeed get a bill, about £50.
One of the things to bear in mind is the question of third party or public liability if you cause accidental damage or injury to someone else not as part of the bike usage. Really is a good idea to have cover if at all possible.