I had my dog insured with AXA for the 6yrs of her life. We had to make some large claims on a couple of occasions and also had to claim ongoing meds costs.
They paid every time and will pay the vet direct.
My only complaint is if you request a claims form it never seems to arrive in the post or it takes several calls to get one! In the end I got one emailed and then saved the PDF to use for next time. Think you can also download them from their website.