
Go to your GP, and
tell h/her you want a second opinion, and you want to go private....most GP`s will have their own list of Specialists who they work with, so they will suggest someone for you to see, but to be honest you are better (through recommendation, by people you know) having a "name " ready, who you would like to see before you see your GP , then you can tell h/her , "I want to see so and so"!
Your GP will give you a letter to take to the specialist , you usually have to make your own appointment , (GP surgery will give you a phone number)
The cost will be depending on what you have done, some Specialists will do the consolations (private) then put you on the NHS waiting list if you cant afford treatment.
The Cost will be "how long is a piece of string" depending on how many times you see h/her, x-rays, blood work.