Generally ATMs give the best rate of exchange, but of course there are user fees... Not as much as the commissions at bureaux de change, though. I'd get some (maybe $100 - $200) worth of Euro and Pounds before you go, so that you have some cash for immediate needs - transit, food, etc. when you first arrive in country. If you can talk your way into getting change or small bills, so much the better, though probably a 20 is the best you'll be able to manage. That's okay, it's easy to get change once you're there.
This takes the urgency out of finding a bank machine when you are tired and swamped with tons of new information all at once. But that works too, in a pinch. I just don't like showing up with empty pockets - seems like I always need money before I can find an ATM.