We have been staying there for years and have tried several different means of getting there from LHR. We have found the fastest means is using the Heathrow Express train from LHR nonstop to Paddington station and then a taxi to the hotel. The HEX takes 15 minutes to Paddington and the taxi is about 10 minutes and about GBP 12 to the hotel. It runs every 15 minutes. Getting a taxi at Paddington is very simple as there is a taxi stand that has a dispatcher. When you get off the HEX turn left as you enter the station and follow the signs- maybe a 3 minute walk. There are reduced fares on the HEX if you buy a roundtrip ahead of time and there is a "DuoSaver" that saves even more if two of you are traveling. Check their website. Discount tickets have to be bought in advance, but you don't have to specify a departure time. The suggestion to use the Picadilly tube line is good if you have only carry on luggage. The HEX is geared towards those with luggage and has lots of room and the seats are very comfortable. The Picadilly line is part of the London Underground and is a mass transit system similar to the NYC subway. It also involves stairs whereas the HEX does not. Using other means such as Uber or a taxi or limo can result in delays as highways from LHR into the city can get very congested at times.