We're with ManyPets (previously BoughtByMany) and I do rate them. We have the most expensive cover with the 15k lifetime. I really recommend getting lifetime as if your dog needs a lifetime medication or treatment it'll cover it. ManyPets cover my dogs teeth cleanings under sedation, most insurers don't cover teeth and that's £250 every 6 months. They also pay for ones prescription which is £70 a month, and we've spent about 2k on a behaviourist for one too which was fully covered.
Were there any situations a claim was refused?
No. They've paid everything no issue, from behaviourists, to dental.
Any companies who really make it all as stress-free as possible?
I've only heard good things about ManyPets, and PetPlan (but they were much more expensive)
Is it better to have a policy where we claim the costs back, or where they pay the vet directly?
It's dependant on the vet too- current vets claim anything over 1k directly from the insurer, up to 1k we pay and they pay us back. Previous vets before we moved you paid everything yourself and claimed back from insurance.
are any policies as all-encompassing as they actually claim to be?
Check carefully. There are very cheap insurers but read the small print.
if a claim is made, does it significantly increase premiums the following year?
Maybe. I started off paying £30 a month when I got one, it went up to £50 last time (he's 4 now) and we've claimed around 5k of things since we got him, so I don't think that's too bad at all.