Can a vet refuse treatment because an owner has no money?

Yes, and No. The RCVS (Royal College of Veterinary Surgeons) which sets standards for vets in the UK states:

17. A veterinary surgeon or a lay member of staff accepting telephone calls must not refuse veterinary attention because the caller is unable to make immediate payment for the treatment. Arrangements for payment should be discussed at an early stage, but immediate first aid and pain relief should not be delayed while financial arrangements are agreed.

18. The RCVS is aware that it may be appropriate to advise euthanasia to relieve suffering, if the owner is unable to afford the fees and is ineligible for charitable treatment.

19. The RCVS has no power to set the fees that a practice charges.

Basically, this means that a vet shouldn't refuse to relieve an animal's suffering in an emergency situation BUT they are under no obligation to provide expensive life-saving treatment if there is no likelihood that they (or their employer) will be paid.

In the old days, when most vets were self-employed, many of them would do what they could for an animal and hope the owner would eventually settle up. It is much more difficult for a young vet who may not have a job next day if he costs his employer money. Add in the crippling levels of student debt which most young vets will have after qualifying and you'll see that they are in an enormously difficult situation if a client turns up with a dog who really needs £800 worth of investigations and treatment but has no money at all.

One of these turned up at 3 am this Sunday morning. The client's dog had collapsed and was pale and shocked. They weren't registered with our clinic, so they had to go to a private vet. Because of the time factor they'd run up a bill of about £130 simply by virtue of walking through the door. They'd got no money at all, and at this point the vet phoned me. Sadly there's just no way we could cover £800 for investigations that might well just reveal treatment would be futile. I offered to cover £200 in the hope that symptomatic treatment might do some good — basically this would mean starting some supportive fluids and antibiotics, but about an hour later they phoned to say the owners had decided the best thing was to put the dog to sleep.