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

https://www.scribd.com/document/1074904087/Private-Hire-and-Ride-Hailing-to-Heathrow-What-to-Know-Before-You-Book-216958

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