Network Rail has put forward a proposal for a Western Rail Approach to Heathrow. This will be a short spur of track in tunnel which would run from a junction east of Langley to the Terminal 5 station, and would permit Great Western Main Line trains to run directly from Slough and Reading into Heathrow, without the need to change at Paddington. The proposal is currently at consultation stage and remains unconfirmed.
(I'm not sure whether this will be acceptable, but I couldn't really think of anything else!)