Pretty much any company will probably do it - it is just a question of cost. You will probably not be able to seperate out the vets bills bit from some of the other bits which tend to come free - like 3rd party liability. But you should be able to tailor any insurance policy.
Persoanlly I would reccommend KBIS or SEIB as both being very flexible on policies. NFU is well regarded on this forum. But steer away from E&L who have a poor reputation.
I would question why you want to insure for vets fees alone - that is actually the element of insurance most people drop rather than isolate.
If you look at threads on here it's also vets fees that the insurance companies try to wiggle out of the most. If you're not insured currently they may well want some kind of vetting and/or vet history and anything you've had the vet to look at (however minor in some cases) will be excluded.
You will be required to inform them of any vet treatment (even if you do not make a claim) and check the small print very carefully - not having up to date vacs/ teeth done regularly etc. etc. can all invalidate the policy (which they will not tell you while you are happily paying premiums but will only come to light once you try and make a claim)
Also when your horse reaches 16 (older on some) most will only insure for accident only not illness.