From Heathrow Terminals 1-3 train to London Paddington, walk to Lancaster Gate Underground Station, Tube to London Liverpool Street, then train to Norwich. 2 h 48 min £72. From Heathrow Airport London bus to Norwich Bus Station. 4 h 20 min £37. From London Heathrow Airport (LHR) drive to Norwich. 2 h 17 min £26.