The RAC says the current petrol price is too high and cannot be justified.
The motoring organisation is urging retailers to pass on recent falls in the wholesale cost of petrol.
It says there is “no good reason” for keeping prices as high as they are and says petrol retailers should cut forecourt prices by 2pence a litre.
But a fuel retailers association said wholesale price and dollar volatility had added to pressures on independent petrol stations.
Asda was the first major retailer to cut fuel prices following the RAC’s claim.
The supermarket giant said it had reduced the price of unleaded by up to 3p per litre and diesel by up to 2p.
The new national price cap means drivers will pay no more than £1.25 per litre for unleaded and £1.28 for diesel at its 318 filling stations.
The RAC says fuel prices have risen almost daily since the end of April, despite wholesale costs coming down by around 2.5p per litre since May 24.
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Average UK forecourt prices currently stand at £1.29 per litre for unleaded and £1.33 for diesel.