Wow, you need to find another bank! My bank charges me about USD 3 for a withdrawal made from another bank's ATM. Are you sure you are quoting the rate for a "bank card" withdrawal, not a "credit card" withdrawal?
Having said that, you will have no problem finding all the ATM's you want between the UK and Hungary, at least. I can't speak for further east along your route because I have not gone there yet. I have been told that Romania has sufficient ATM's as well, but just in the larger cities.