For England: You can usually chose your doctors in the NHS. Here's the patient facing info: https://www.nhs.uk/using-the-nhs/nhs-services/hospitals/nhs-...

Here's the bureaucratic document for commissioners of general practice (primary care doctors) (sorry you need to ctrlF for "choice".) This document also tells you where in law patient choice is detailed: https://www.england.nhs.uk/publication/primary-medical-care-...

> and I have no recourse.

If the treatment is negligent and causes harm you can sue. There are cultural and legal differences, but suing the NHS is possible.