Richmondshire's 22,885 householders are among the few across the country to benefit from a freeze in their district council tax.
District Councillors have confirmed that its portion of the annual tax will remain unchanged for the next 12 months.
People in Hawes in North Yorkshire and the NE48 postcode area of Northumberland are to see cuts in fuel prices at local garages.
The Government is extending its rural fuel rebate to 17 more areas across the country which will cut 5p off every litre of fuel.
The scheme has been set up to help people who are currently faced with some of the highest petrol prices in the country. It will run for six years before it is reviewed.
The cost of fuel is "particularly high" in "very rural areas", a government minister has told ITV News Tyne Tees.
Treasury Minister Damian Hinds was speaking on the day that a 5p cut in the cost of fuel comes into effect in 17 areas across the country, including Hawes in North Yorkshire and the NE48 postcode in Northumberland.
The government say the move is because they understand the extra costs that people in rural communities can face but they could not guarantee that the scheme will be extended beyond an initial six years.
Police are appealing for witnesses after a motorcyclist died in a collision near Hawes on September 14, on the B6255, Hawes to Ingleton Road, three miles south of Hawes.
The motorcyclist, a 59-year-old man from Penrith in Cumbria, was riding a silver Honda Blackbird and travelling away from Hawes when he was in collision with a grey Toyota RAV 4 which was travelling in the opposite direction.
The motorcyclist was travelling with a group of three other bikers when the collision happened.
Anyone with any information is asked to contact North Yorkshire Police on 101.
The eyes of the world won't just be on the Tour De France cyclists this weekend, but also the cities, towns and villages along the route. Jonny Blair spent the day Hawes in North Yorkshire to see how the town is preparing to play its part in history.
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.