I want to share our success using the TfL train into London. Last trip we didn't know about it and suffered through the long subway ride.
When we arrived we took the TfL train from Heathrow Terminals 2 & 3 to the Ealing Broadway underground stop, using our Oyster cards that we had bought right there in the Heathrow terminal; we then transferred to the Central underground line to take us to our southbound railway train at Charing Cross for our first excursion out of London. (You can also stay on the TfL train until Paddington to connect to other lines - fares, travel times, and more information on the TfL and Heathrow Express trains here: https://www.londontoolkit.com/travel/heathrow_connect_train.htm )
The TfL train from Heathrow uses the same tracks as the Heathrow Express, but it is much cheaper because it stops a few times and the Heathrow Express doesn't stop at all. Because these 2 trains leave from the same station/platform at Heathrow, you have to be careful which one you are getting on. There is a lighted sign telling you which train is arriving next, and when. There is also usually an employee on site to help you get on the right train. On the train a conductor will come around with an electronic reader to check your Oyster card and make sure you have enough cash on it to make the trip.
Upon your arrival at Heathrow, there are so many salespeople and kiosks hawking the much more expensive Heathrow Express, it is easy to think that the Heathrow signs that say "to trains" are referring only to the Heathrow Express. But no, they refer to both the TfL AND the Heathrow Express. Don't be afraid. Follow the signs to the trains!
The TfL train costs a little more than riding the underground all the way from Heathrow into London, but it is much faster, and way easier if you have luggage. In fact we were also able to use this system when we returned to Heathrow to fly home. We left early (about 6.00 a.m.) from our hotel near the Central line, walked 2 blocks to our underground station, got on a westbound train and went 5 stops to Ealing Broadway, got off the underground, and went directly to the TfL train platform. (At this point if you make the mistake of touching out from the underground you will have to immediately touch back in for the train which costs another fare - we actually made this mistake but the staff helped us and kept us from having to pay additional. Always ask for help.)
The whole trip to Heathrow from our hotel, including the walking, was 45-50 minutes; we arrived 3.5 hours before our flight and had plenty of time for security lines and a leisurely breakfast. Of course, depending on how early your flight is this system might not work because the trains might not be running yet - the link above also includes daily start times for the TfL and underground trains.