Hi! If you will look at the left side of the screen in the resources section, there is a "Find A physician" area that has a number of doctors in Great Britain. Since you have the internet, you might also consider e-mailing Dr. Milton Waner, in NYC. I know that he trained a # of surgeons from the UK and he might be able to direct you.
My daughter has a lymphatic malformation. She has never mentioned it hurting except after surgeries and once when she had an infection. I can imagine an AVM involving a limb would be painful due to the veins being involved.