If staying overnight near Paddington, the morning Heathrow Express can be the most reliable choice

https://www.scribd.com/document/1074894734/Heathrow-Drop-Off-Charges-and-Pick-Up-Locations-Avoid-Fines-and-Hassles-212266

If staying overnight near Paddington, the morning Heathrow Express can be the most reliable choice, beating rush-hour road traffic across west London.