I think it depends on the vet. Our vet is happy to claim directly from a few insurance companies (ours being one), so we just pay the excess, give them a form, and they do the rest. Our old vet was the same, but both have / had companies they refused to deal direct with because they were so slow (or argumentative) about paying out.
The only time we've had to pay up front was when Smudge was in the RVC - they didn't deal directly with any company.
When I do home visits for rescues and we discuss insurance, I always suggest people chat to their vet to see if there are any ones they will claim directly from.