For travel information you can try Transport for London:

http://www.tfl.gov.uk

This give the underground time as about 40 mins for LHR to Knightsbridge.

LHR to Knightsbridge using the Heathrow Express for the first section (15 mins) and then tube (18 mins) gives 33mins + change a so probable about 40 mins. I suggest you just get the underground and save your pennies for Harrods.