David Bennetts wrote to uk.transport.london on Mon, 4 Apr 2005:

If you're going to South Kensington it'll be far cheaper, easier and
probably quicker to get the Heathrow Express to Terminals 1,2,3 (free) and
change to the Picadilly Line tube there. Then change to a district line
train at Barons Court (across platform connection).

No need to change - Piccadilly Line stops at South Ken too!
--
"Mrs Redboots"
http://www.amsmyth.demon.co.uk/
Website updated 3 April 2005