There is huge variation in the amount of cover provided by private medical insurance policies with some having restrictions on where you can have treatment and by whom.
If you are using your private medical insurance it is your responsibility to ensure that you have cover in place for your treatment and you are personally responsible for covering the cost of any shortfalls.
For this reason it is vital that you contact your insurance company prior to booking your appointment to check that your policy covers Mr Bankes and the hospitals where he practices, namely:  

The London Clinic, 20 Devonshire Place, London, W1G 6BW

Fortius Clinic, 17 Fitzhardinge Street, London, W1H 6EQ

The Hospital of St John & St Elizabeth, 60 Grove End Road, London NW8 9NH
Only your insurance company can give you this information. 
At the time of booking your appointment you will be asked to give your insurance details, membership and authorisation number.  If you are unable to do this you will be treated as a self-pay patient and asked to settle your bill directly at the point of treatment.