I was told by the lady at the Tavistock and Portman Clinic that, realistically, the earliest I would be able to have top surgery with the NHS would be age 24.

(My mother says this means that my surgery would be free)

If I had the funds to go private, would I be able to have it at age 18? How would I go about this? How much would it cost (roughly)?

I live in U.S., so I don't know how things work over there.  and I am pre-op, so this is only from the research I've done.  Top surgery over here only costs like $6,000, minus any expenses such hotel or transportation. 

And I see no reason why you couldn't have it at age 18, as long as your therapist gave it a go.  At least over here.

I'm not sure but a quick google search brought up this: http://www.transgenderzone.com/ftm/surgery.htm but I'm not sure how old or reliable it would be.  I see no reason why you would be denied surgery as long as your councillor was happy and your surgeon was as well.  It's a long way off for me and I'm pretty sure I'll not be able to afford to go private so I've not looked into it.