I don't think so.  The NHS is for everybody.

There might be an issue if the drugs being used would interact with the treatment in some way, but even that shouldn't trigger a downright refusal to treat.

Thanks so much, was wondering as it's a family member of mine.

Here are a couple of summaries of your NHS rights: NHS Treatment - your rights and NHS Patients' Rights - Citizens' Advice

The only mention I can find of a hospital refusing to treat a patient is in the second link, but that only applies when a patient is violent or abusive, and even then treatment can't be refused for life threatening conditions.