Justice of the Peace is a free service and they do visit Citizens advice bureau, contact your nearest one and they will let you know what times they are available. Had to find one recently and had no idea how to go about it either! I had to wait ten mins or so in a queue, but that was OK.
Are you working? If so someone in your office may well be one, or have a relative that is, thats how hubby found one to witness his documents.
Or as above, pick one out of the yellow pages!
Edit...
Helps if I read properly, eh! I wouldnt think you would be able to get it done at the airport though?