Heathrow has Internet machines almost as often as they have pay phones, so at least I could send email. It cost a pound for 15 minutes. GAH!
I did buy some time at Gatwick, some years ago, but at lower rates. Everything conspired against me on that trip -- the hotel hadn't put in their free WiFi yet (other hotels in the chain had it), the wired Internet was too expensive, the cellphone Internet pricing was too high, and I couldn't connect via the hotel-room phone.