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."
Chief Treasury Secretary Danny Alexander's constituency at Inverness, Nairn, Badenoch & Strathspey would benefit from the scheme. He put forward his views:
Hawes in North Yorkshire is among ten areas that could benefit from a 5p-per-litre fuel duty cut.
The Government has applied to the European Commission to vary the duty rates.
Discounts have never been permitted before, but Chief Treasury Secretary Danny Alexander said the 'strongest possible evidence' had been put together to make sure an extension goes ahead.
Hawes was chosen because it has higher pump prices than other locations that already receive a discount. It is also more than 100 miles from the nearest refinery, and has a population of fewer than 135 people per square kilometre.
The commission is expected to announce its decision next year.
Drivers in Hawes in North Yorkshire could see their fuel prices cut. It comes as part of the UK's application to the European Commission to extend the rural fuel rebate scheme.
The town was judged to meet strict criteria, for example showing pricing similar to that of islands currently eligible for discount.
The UK now needs to gain approval for the expanded scheme from the EC. If approved, it could cut up to five pence from the price of a litre.
The final decision on the scheme is expected next year.
Government plans to reduce fuel prices in rural areas have taken a step forward.
Fuel retailers in remote areas are being asked to let the government know how much they charge for petrol and diesel. The government is preparing to ask the European Commission for permission to extend the existing Island Fuel Rebate Scheme to remote rural areas on the mainland.
Areas that would be affected:
- North Yorkshire
Around 300,000 more homes are likely to have been pushed into "fuel poverty" by Christmas, a campaign group has warned.
The Fuel Poverty Advisory Group says six million people are now struggling to pay their energy bills.
It comes as the industry regulator Ofgem announced a multi-billion pound network upgrade, adding yet more to the bill of every consumer.
Stephen Douglas reports:
Citizens Advice in the North East is urging families and households to save money on their fuel bills during Big Energy Saving Week. People here spend less on food to pay for their other bills than anywhere else in the country. **
The service is hoping people will consider what they can do to help themselves and is using this week to call on them to consider switching energy suppliers and to look at ways to insulate their homes**
Campaigners are putting pressure on the Government to cut duty on fuel. The Tax Payer's Alliance and the Petrol Retailer's Association are setting up stands on independent forecourts to ask motorists to lobby local MP's.
Sixty pence in every pound spent on petrol or diesel in the UK goes to the treasury. UK has the highest tax on unleaded petrol in the EU.
Forecourt owners like Allan Glendinning in Prudhoe, in Northumberland, say the situation is desperate.
Campaigners against high fuel tax will be on forecourts across the region this morning to tell customers how much their petrol costs and how much money is going to the Treasury. Over 5,000 stands will be set up across the country.
Businesses have welcomed the announcement by the Chancellor that fuel duty will not rise by 3p in August.
It could ultimately benefit consumers, by preventing an increase in the cost of transporting essential goods.