The supermarket chain has lowered the price of unleaded by up to 3p a litre, meaning drivers will pay no more than £1.25 per litre at Asda’s 318 filling stations.
Asda has also cut the cost of diesel by up to 2p, introducing a national price cap of £1.28 per litre at its outlets.
RAC spokesman Rod Dennis welcomed the news, saying: “At last, retailers have done the right thing and started to cut prices at the pumps.
“From our data, we could see no justification for them holding on to savings that they have been benefiting from for three weeks.”
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Earlier this week, the RAC called for forecourt prices to be reduced to reflect the recent fall in wholesale fuel costs.
With the United States drilling for more oil than in recent years, and Russia increasing its output, the price of oil on global markets has been falling since the end of May.
Yet according to data from RAC Fuel Watch, drivers have endured a rise in forecourt fuel prices almost every day since the end of April.
This has left average UK petrol and diesel prices at their most expensive since September 2014. On Monday a litre of unleaded cost a hefty £1.29 on average, while a litre of diesel was an eye-watering £1.33.
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But now Asda has taken some action to relieve the strain on hard-pressed motorists, and other UK supermarkets can be expected to follow suit.
The RAC’s Mr Dennis says: “With petrol prices rising at their fastest rate in 18 years last month, millions of households and businesses will have been feeling the effect of having to spend more on what is an essential purchase for many. Today's cuts should bring some welcome relief.
“It is absolutely right that at times when wholesale prices are falling, forecourt prices follow suit.”