Asda has announced a national cap meaning motorists will not shell out more than 105.7ppl on unleaded and 106.7ppl on diesel across their 272 stations.
Tesco rolled out a 2p drop that will come into effect from 5pm on Monday.
Peter Cattell, fuel director for Tesco, said: “We know that lots of customers will have plans for the summer holidays, so we’re dropping the price of our fuel to help them enjoy it even more.
“This reduction of up to 2p per litre on petrol and diesel at all our 500 petrol filling stations will mean millions of customers save money by shopping at Tesco.”
Andy Peake, Asda’s senior director for petrol, said the chain has dropped the price of fuel because it is the start of the summer holidays and “families will be getting out and about”.
He added: “At Asda we always pass on any savings we can make to our customers, so it’s great to see that costs have dropped despite early predictions that the cost of fuel would increase following the outcome of the EU Referendum.”
Last week, Morrisons kicked off the price cut by reducing the price of unleaded by 2p a litre - also cutting up to 1p a litre off diesel.
Roger Fogg, Morrisons’ services director, said at the time: “Among post-Brexit fuel price uncertainty, we are doing all we can to hold down prices for our customers.
“When we can make savings we will pass it on to customers.”
Recently, oil has hit around 43 US dollars a barrel, the lowest level since early May.
In July the RAC said the price retailers pay for fuel had been falling for almost a month but pump prices remained largely static over the same period.
They claimed there was a “compelling case” for a forecourt reduction and hoped retailers were not taking advantage of public perceptions that fuel prices would rise after Brexit.
RAC spokesman Simon Williams praised the current price drop, but said it is a shame it “did not come sooner”.
He added: “This price cut takes us back to a supermarket price that was last seen in early May. Hopefully other supermarkets will follow suit which will drive prices down across the country.
“If that happens we should see the average price of both petrol and diesel drop from around 112p a litre to 110p.”
Luke Bosdet from the AA added: “Drivers are in a good place with pump prices this summer, paying as much as 5p a litre less than a year ago.
“However, with the weaker pound, it’s more a case of pump paradise lost than pump paradise found.”
He said had the pound regained last summer’s value against the dollar, summer petrol prices in the UK would be at its cheapest for seven years.