By Underground: (Strongly Recommended)
The Piccadilly line serves Heathrow, with trains running every few minutes from early morning to late evening. The journey time to Victoria is roughly one hour. Take the Piccadilly Line to Hammersmith and then on the opposite side of the same platform onto the District Line to Victoria Station. Make sure that the train goes to Victoria Station. DO NOT board trains to Edgware Road or Kensington Olympia.
Once you arrive at Victoria, follow walking directions listed above, with the aid of the map by clicking on the link above.
By Rail and Underground:
The Heathrow Express runs direct, high-speed trains between Paddington Station and Heathrow. Trains depart every 15 minutes and have a journey time of 15 minutes from Heathrow Terminals 1, 2 and 3. Allow an extra 5 minutes for journeys to and from Terminal 4. At Paddington take the Underground District Line to Victoria Station. Follow walking direction listed above.
National Express coaches and Airbus run to Victoria Coach Station every 30 minutes. This is a very good option as the Victoria Coach Station is located literally around the corner from the Winchester Hotel. Cost will be roughly £7.00 standard single. The journey time may ranges between 45mins and 90mins, depending on the traffic. Recommended for late night arrivals.
Journey time takes approximately 40 minutes to one hour and costs roughly £40-£50.