Your knowledge of London transit is shockingly bad. There is an express rail connector from Heathrow to Paddington that costs around 15 pounds and gets you int

Your knowledge of London transit is shockingly bad. There is an express rail connector from Heathrow to Paddington that costs around 15 pounds and gets you into London in about half an hour. If you have more time you can take the Picadilly tube line from Heathrow to Victoria station in about an hour. More stops and less room for luggage on the tube, but it will cost less. Crossrail is not about connecting heathrow, it is to connect the southeast with London, the phase II link to Heathrow is just bonus. In fact, it will use the exact same line as the heathrow express uses now when it goes from Paddington through Heathrow and further west. A crossrail link just means you don't have to switch trains at Paddington to finish the trip to Heathrow if you started in the SE commuter belt.