I worked at WLT between 1978 and 1980 when the BABS (pre-Amadeus reservations system) mainframes lived there.
IIRC the check-in and bus service had already stopped by then. As posted above, the building was demolished and the site on Cromwell Road is now occupied by Sainsburys.
From
http://www.tfl.gov.uk/corporate/mode...cts/13175.aspx
In more recent years, the Piccadilly line was extended west from Hounslow West to serve Hatton Cross (1975) and Heathrow Terminals 1, 2, 3 (1977). In 1986, the Heathrow service was developed into a loop, to serve the new Terminal 4.