Film is cheap in comparison to things like flight costs and accomodation. Bring some with you and if you need more get it from a reputable source, Jessops, Silverprint, Mr Cad (if you can get to Croydon that is one great day out in their store!) or Calumet.
Get film from places that have a good turnover of film i.e. fresh.
I don't think you need to worry with x-rays with slower film speeds in hand luggage, hold luggage is subject to much higher doses of radiation though. Asking for a hand search may be acceptable to airport staff if they are not busy but is not a right you have. Lead type film cases are not a good idea. If they cant 'see' through the film case they may put it through the x-ray at a higher dose. (info from Mum, just retired Gatwick BAA security).
I hope you have a top time in London Paul.