A couple of thoughts:

1. Most US Admiral's Clubs have free net access (assuming the computer's up, which is not a given since any public computer gets messed up regularly, and that you can get to it) but not overseas. Both London clubs (LHR and LGW) do have pay-as-you-go access, though.

2. The Heathrow Hilton has computers in its business floor rooms. I don't recall the technology but it includes Net access. You pay for some amount of use in advance and the meter runs as you use it (faster when you're printing).

3. Many hotels - the Concorde-St. Lazare in Paris comes to mind since I was there last week, but others too - have business centers where guest can use computers at reasonable rates.