Saxon clinic appears to be BMI, not BUPA owned. although BUPA have contracts with them.
Usually BMI or other private hospital providers are providing the room and clerical support, and the Consultant is not working for them but is self-employed for that element of their work, but may be reimbursed by BUPA if they are your insurers.
So… follow the money…
If your consultation was paid for by your insurers, I’d possibly contact them and complain, with a copy to the Consultant.
If you are paying for the consultation yourself, I’d initially write to the Consultant himself, setting out your complaint. If you are unhappy with the outcome, contact the manager of the Clinic.