Hawes in Upper Wensleydale has a population of just over 1,000.
There is only one petrol station in the town, and it has higher pump prices than other locations that already receive a discount.
If it were to close, drivers say they would face a 34-mile round trip to fill up.
That's why it's been chosen as one of 10 areas that could benefit from a 5p-per-litre fuel duty cut.
Chief Secretary to the Treasury Danny Alexander said: "As a Highlander, I know all too well that fuel prices tend to be highest in areas where a car is needed the most."
More top news
The sister of England footballer Jill Scott from Sunderland, says she 'couldn't be prouder' of the team, who lost in the World Cup semis.
Victorian North Yorkshire railway station celebrates 150 years of operation
Newcastle International Airport has welcomed the recommendation by the Airports Commission that a third runway should be built at Heathrow.