Gday J!
I had the same problem trying to work out how I was going to get from Heathrow to Kensington.
We’re going to take the Heathrow Express direct to Paddington and then a 10-15 minute cab ride (as opposed to a rediculously long one) from there.
You can even pre-purchase your ticket online 
Here’s the site for the Heathrow Express: http://www.heathrowexpress.com/index.asp
Sorry to butt into your conversation, but I LOVE to help!
Cheers
Trish