I don't know about driving in London, so I will let those who live there give you advice, but I would think to just go via public transportation from Heathrow- but then you do have to go back to Heathrow I take it? Is Heathrow easy for you husband and where you're travelling onto next.
How much time do you have? If you wanted to go via tube or train that's quite easy. have a fair bit of time, take the Picadilly line to the Bakerloo line, bob's your uncle.
Otherwise, you could get the Heathrow Connect or Heathrow Express to Paddington and get on the Bakerloo line as well.