Try
http://www.transportdirect.info/Web2/JourneyPlanning/JourneyPlannerInput.aspx .... Awesome transport planner that I swear by! It'll tell you how to get from your own house door, all the way to Karidis' clinic by train, coach and then even tells you how to get around London with the Underground, etc! For reference, you can use "NW8 9NH" for the hospital address when using planners and stuff.
Taxi's in London are not only expensive, they usually take forever to get anywhere due to congestion. The Underground is cheap and quick (when it's working!). For around a tenner you can get a day ticket for zones 1-3. It should only take you around 20-25 minutes I reckon to get from Euston to St Johns Wood Underground station (which is literally 1 minute from Karidis).
EDIT: It's only 3 miles from London Euston to Karidis apparently, I can imagine that'll take like 15 mins minimum to drive in London, but if you're not comfortable getting the underground you might find you can book a private taxi and negotiate the fee beforehand for about £10-15.Consultation is very speedy and efficient. I felt a little disheartened as I did feel a little rushed. They only start treating you like gold when you start giving them money! (typical private practice
) But in terms of time, my consultation took 30 minutes or so. I had lots of questions for Karidis and even some pictures that I found online of people with cratered nipples and stuff. He really put me to rest and told me those pictures were due to the work of amateur surgeons and he laughed when he saw them!
For transport, maybe look at getting a coach? They're really not that bad, you can get National Express coaches for around £8 and if you're lucky Megabus.com sometimes goes as low as £2 to London!
Definitely arrive early at the hospital, the staff are helpful but the place was way bigger than I would've thought. I'd say 40 minutes early is definitely a good idea, you may even get called in early.
And congrats on taking the first step mate! It's a crazy and exciting journey with an awesome outcome, you won't regret it - I haven't.