I second what Patrick says above, but don't know Heahtrow Express from personal experience.

When we (2 in our 50's and fine shape) had B&B in Belgravia less than 10 minutes from a Tube stop along the Picadilly Line (which is the one from LHR), we took the Tube (each had a 24" roller and a backpack). Took about 70 minutes; worked great; cheap.

When there were 3 of us (us plus 21-yr-old daughter) and our B&B was in Bayswater, only 5 minutes from the Tube stop but not on the Picadilly Line, so there would have been a transfer, we used justairports. We each had roller plus backpack. Took about 70 minutes; worked great; worth the cost for the absolute convenience of pickup and delivery (and pickup at the door upon return to LHR).

So either works; if your rooms aren't far from a Tube stop on Picadilly Line, then I'd say save the money and do a teeny schlepping. If not, or you have some other mobility, luggage, or timing concern, then booking a car service is wonderful. Pre-book!