There are now three trains into central London from Heathrow.
- The oldest, slowest, and cheapest is the Piccadilly line on the tube: 5.60 pounds, about an hour to Paddington
- 20 years old, fastest, and most expensive is Heathrow Express: 25 pounds, about 15 minutes to Paddington
- Two years old, in between on speed and price is the Elizabeth Line: 12.20 pounds, about half an hour to Paddington
The tube and the Elizabeth line do not require tickets. Just tap your credit card and go.
Heathrow express ends at Paddington the others get closer to Euston (but not too Euston) for a shorter cab ride, tube ride, or nice walk. I'm +1 on the fly to LHR, train to Edinburgh, it is a really beautiful train ride.