[Symbiote]

A London Underground fare, off-peak, avoiding Zone 1, is also £1.50.

So, Heathrow Terminal 5 to Epping should be a contender. It's around 28 miles.

(And being run by a private company can't exclude MegaBus, since almost all public transport in the UK is run by private companies.)

[wopian]

Yup Terminal 5 to Epping is possible for £1.50 (2 routes bypassing zone 1). Else its £5.10 direct through zone 1.