I've just discovered (via the London Tube Flickr group) this:
http://www.tuberelief.co.uk/ - "In late August 2005, we are are going to go round all the London Underground stations in one day..."
They aren't giving out the exact date, but I have now emailed to sign up and find out if the date is doable. 242 stations and walking about 10km. You should all do it as well.