In some countries, anyone using a debit card (other than customers of the bank which owns the machine) will be charged a fee by the machine's owners. (For a short while, UK banks tried to introduce a similar system here). So there's no way that you can avoid those charges.
However, in most countries there's no charge made by the bank which owns the machine. (Although, just like the UK, you need to ensure that the machine is actually operated by a major bank. There are also independently operated machines which do make a charge, just like the ones you find in many convenience stores in the UK).
The UK bank which has gained a considerable number of customers, through its policy of not charging for overseas cash withdrawals, is Nationwide. Their FlexAccount is frequently recommended by the travel press (and by BBC consumer programmes), as well as by AB contributors, for travellers who wish to use overseas ATMs:
http://www.nationwide.co.uk/current_account/de fault.htm
Remember that there aren't as many ATMs in many foreign countries as you'd find here in the UK. For example, LIverpool Street station has got 14 platforms and there are at least as many ATMs around the station. Gare du Nord, in Paris, has over 50 platforms but it's got just one ATM!
Chris