Surgeon? Medical? What specialty?
EDIT: Just seen endocrinology
Well, it depends on the consultant - it can cost around £200 for the initial consultation and £100 for followups thereafter. If you go private and are self-funded, you will be expected to pay for ALL treatment including any scans (at least I think so), where things like MRIs can amount to £1000.
You can have your first few consultations privately then ask to be switched to the consultant's NHS list.
TEN WEEKS is a very long time to wait!!
Private treatment is usually offered at a different hospital such as BUPA. Ring the consultant's secretary. If he/she knows the number of the consultant's private secretary he/she will be able to give you their number and you'll get the ball rolling quickly. Usually about 3 weeks.