We have the beasts insured with More Than, and they've never quibbled about the ginormo-bills that Robot Tabbyface racked up when in Cat Hospital, or the hefty bills from the emergency vet when Bear had to be emergency-looked-at, or any amount of other stuff. They are not the cheapest about, and there's a reasonably large excess on older cats (£100-ish? I can't remember), but they have been swift at processing claims. They are happy to insure Battersea beasties, and I think (not sure on this) happy to insure all ages of beast. I have no idea how they compare to others these days - they were good value when I got my lot, but there weren't so many options then.
Pet Plan are very good indeed, from what I know, and deal directly with the vet rather than you needing to pay and claim, but they're also very expensive.