Petrol prices have hit record highs in the UK this year as the rising cost of oil caused increases at the pumps.
The UK saw the worst monthly rise in the average price of petrol in at least 18 years in May
Oil broke through the $80 a barrel mark twice in May – something which has not been seen for three and a half years (since 12 November 2014).
However, Asda has not cut the price of fuel following claims that retailers were not passing on savings to drivers.
The supermarket giant slashed 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.
UK motorists have suffered a rise in fuel prices for almost every day sine the end of April, despite wholesale costs dropping by 2.5p per litre since May 24th.
Wholesale costs have been reduced due the US drilling for more oil than in recent years, says the RAC.
On Monday, average UK forecourt prices stood at £1.29 per litre for unleaded and £1.33 for diesel - the most expensive both have been since September 2014.
Asda chief executive Roger Burnley said: "We know that the cost of living is centre of mind for our customers and we will always do whatever we can to reduce that burden.
"Customers can trust us to lead the way when it comes to lowering the price of fuel and putting cash back in their pocket."
RAC spokesman Rod Dennis said: "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.
"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."