It comes after fuel retailers were accused of not passing on savings from lower wholesale costs.
Asda said its new national fuel cap means drivers will pay no more than 122.7p per litre at its 319 filling stations.
Asda's senior fuel buyer, Dave Tyrer, said: "Our new national price cap of 122.7p per litre will be welcomed by the millions of drivers across the UK.
"Further decreases in the wholesale market mean we are able to reduce our prices again, seeing our unleaded price dropped by up to 5p per litre in just under two weeks.
Ashley Myers, Morrisons head of fuel, said: “We’re passing on savings from falling wholesale costs and keeping our fuel prices far below the UK average.”
Both petrol and diesel prices have reached a four-year high in recent months.
Three ways to cut your fuel costs
- Accelerate gradually without over-revving
- Always drive on the highest possible gear
- If you can, allow your car to slow down naturally as your brake is a money burner
- Re-starting your car is expensive, if you can, keep moving
Over the past six months the cost of filling up a typical 55-litre family car that runs on petrol or diesel has risen by around £6.
The RAC recently said drivers should "feel aggrieved" after average petrol prices remained virtually unchanged last month despite a fall in wholesale costs.
It claimed the biggest retailers who sell the most fuel have "taken drivers for a ride".
AA fuel spokesman Luke Bosdet said: "With 4p knocked off the wholesale price of a litre of petrol through October, the AA has watched with dismay as average pump prices have trickled down by barely a penny.
"Some supermarkets have chosen to pass on the savings as money-off offers – but only if you spent £60 or so in store.
"Asda, as usual, will break the log-jam by cutting prices for all drivers and forcing other forecourts locally to follow suit.
"Sadly, beyond those areas, the pump prices will stay high as other retailers choose to hang on to the savings they should be passing on to hard-pressed consumers."
Yesterday, it was revealed the police bosses want petrol companies to make drivers pre-pay for petrol to help stop fuel thefts.
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