According to comparison site, Gocompare.com, 3.5 million motorists will drive up to 10 miles out of their way to save 5p a litre, while 2.5 million will drive 20 miles or more for the same saving.

However, drivers are being warned that even a Ford Focus 1.6, driving just nine extra miles could cancel out any benefits.

At current fuel prices, driving a petrol engine car with an average combined fuel efficiency of around 45 miles per gallon for more than an extra 10 miles cancels out the benefit of a 5p per litre saving on an average £38.81 top-up.

None of the figures take into account the additional time it takes and the extra wear and tear on your vehicle and tyres.

Scott Kelly, head of motor services at Gocompare.com, said: “With fuel prices heading up again it’s not surprising that motorists will go out of their way to find cheaper petrol and diesel.

“However, what this research shows is that millions of motorists could be spending more on fuel in the hunt for the most competitive petrol stations, than they stand to save on their fuel when they get there.”

Gocompare.com believes that with a car’s fuel consumption rated in miles per gallon (MPG) and fuel sold in litres, many drivers find it difficult to calculate how many miles they can drive for their money.

Just 13% of drivers know how many miles they can drive per litre of fuel compared to 41 per cent who know their approximate MPG.

Kelly added: “For drivers getting less than an average of 45 MPG from their car, an extra 10 mile round trip to get cheaper fuel could result in you paying more for an average top-up.

“And the 2.5m drivers who would travel 20 miles or more out of their way for a 5p per litre saving would almost certainly lose money.”

Consumers who do want to drive around to find the best deal are advised to fill up as much as they can afford so that the distance driven is worth it and makes the minimum dent to their spend.