Prior to its potential closure in January last year, the 840 was voted the most scenic route in the UK by an online poll organised by Bus Users UK in 2018.
The introduction of the £2 fare cap salvaged the route, which benefited from a resurgence in demand for bus-based breaks and day trips.
Mr Burley said: “It just took off. The profile of the 840 was already high, but now it was also much more affordable. We had people write to us saying they’d just taken the bus and that they were complete converts.”
The route takes in York and the market towns of Malton and Pickering before climbing on to the North York Moors, where it runs via Goathland, which doubled for the fictional village of Aidensfield in 1960s-set police drama Heartbeat and remains a huge draw for tourists.
From there it descends to the coast at Whitby, with its bustling harbour, award-winning fish-and-chip shops and a ruined abbey that inspired Bram Stoker to write Dracula.
Other picturesque routes that have experienced a surge in popularity since the fare cap was introduced face a similarly worrying future should it be allowed to expire in December.
While industry and Whitehall sources suggest that Ms Reeves will initially lift the cap to £2.50 and then £3, the expectation is that it will be gone altogether by the start of 2026.
Rural services will be hit far harder than urban ones, the Confederation of Passenger Transport trade group predicts, since the level of subsidy required is far higher.
Stagecoach’s 555 service, which takes more than three hours to travel the 50 miles between the city of Lancaster and Keswick in north-west Cumbria via the heart of the Lake District, is of such renown that it has its own Wikipedia entry.
Ridership on the 555, operated by open-top double-deckers, has increased 10pc this year, even though tourist numbers in the national park have declined 10pc. Such growth is unlikely to be maintained if the cap is removed and previous fares of £11 each way are reintroduced.