Depending on where you’re headed in London I highly recommend booking a ticket on the Express. It’s cheap and you can do it online. You can even book it with a round trip for your return heading out. It’ll get you into Central London in a matter of minutes with no stops direct from the airport. From St Pancrass Station you can then get just about anywhere on the Tube. Way, way faster and cheaper than every other alternative, and you hop on the train immediately inside Heathrow. Piece of cake!