After checking out of the DoubleTree London West End we wheeled our luggage a couple of blocks (0.2 miles) up the street to the Russell Square London Underground Station. From there we took the Jubilee line direct to Heathrow Airport Termina 2, a ride of about one hour.
If we had to change trains we probably would not have taken the London Underground to the airport but it just happened that the line that served the station closest to us goes direct to the airport without any change of trains. The Jubilee Line trains actually have spaces reserved for luggage since they know many people use that train to get to and from the airport. Our hotel was right in the middle between the Russell Square Station and the Holborn Station but the Holborn Station had a lot more up and down steps than the Russell Square Station. The Russell Square Station has a lift (elevator) from the street level almost down to the platform level. There were still about a dozen steps after the left to get to the platform level but it wasn't too hard to carry the luggage down the steps.
The trains were pretty crowded but they run about every 5 minutes. We let the first train go by as it was too crowded to get on. The next train wasn't quite as crowded and one of the areas designated for luggage was available. We were not immediately available to find seats but the train quickly started getting less crowded as we headed away from central London. It wasn't long before the 2 seats nearest to our luggage became available and so we had seats for the rest of the ride to the airport
There is an express train to the airport but we would have had to take a taxi or Uber to get to the train station where it departs from in London. The is a new Underground line that will go directly to the airport called Crossrail that is supposed to open up in the next year or two (2019 or 2020). It appears that a station on that line is being built half way between our hotel and the Holborn Underground Station. If in the future we stay at the same hotel or any hotel in the Russell Square area, then we will probably use the new Crossrail Line to get to and from the airport.
Taking the London Undergrond or the Express Train is almost as fast as taking a taxi or an Uber because of all the delays from London traffic. But, the Underground and the train is a lot less expensive. The Underground is less than 5 GBP per person whereas a tax or Uber or a private car hire can easily run 50 GBP or more.
We had departed the hotel about 3 hours before our flight. We really should have departed 4 hours before our flight. The Heathrow Aiport has an excellent United Airlines Lounge with all sorts of food and drinks. We were hoping to spend some time there and get some breakfast. But, it took us a lot longer to get through airport security than we expected. TSA Pre-Check does not apply to airports outside the United States so I had to remove all my portable electronics from my backpack and place them on the X-Ray tray. My wife's backpack got set aside for more detailed inspection so that added quite a delay. By the time we got through security, it was only about 30 minutes before our flight would start boarding. We noticed a sign that said that it was an 18 minute walk from Security to the area of our gate! Thus we pretty much had to spend what time we had left just walking to our gate. There was no time to stop by the United Lounge.