If you are travelling to T4 you can use the free shuttle bus from Hatton Cross tube station, or the free shuttle service on the Heathrow Express from the Terminal 1,2,3 tube station.
Tube passengers travelling to and from Heathrow Terminal 4 will be using a dedicated bus shuttle at Hatton Cross from January 7, 2005 for 20 months.So that'll all be bloody awkward...
The change from Tube to bus is to allow for construction of the Piccadilly line extension to the new BAA Heathrow Terminal 5. London Underground's (LU) Heathrow Terminal 4 station will remain closed during the work.
Piccadilly line services will continue to run direct to and from central London to Heathrow Terminals 1, 2 & 3 station. The change will mean a slightly increased journey time to Terminal 4 of five to ten minutes. But it will actually cut journey times by Tube to Heathrow Terminals 1, 2 & 3 by a few minutes.