Supermarkets in Bristol have cut petrol prices for the second week running as the fuel war intensifies.

Morrisons, Tesco and Asda have all announced a 2p cut in the cost of a litre of unleaded and a 4p cut on diesel.

Across the country, unleaded at Sainsbury's is up to 3p cheaper, and the cost of its diesel has been cut by up to 4p, in addition to their current promotion of 5p off per litre when customers spend £50 or more in-store.

The latest cuts continue a price war sparked last week, when Asda cut 3p from diesel and unleaded – which swiftly provoked similar drops from Morrisons, Sainsbury's and Tesco.

In two weeks, the Morrisons store at Lysander Road, Cribbs Causeway has sliced nearly 7p off the pump price of its unleaded, which now stands at 110p. Its diesel is now 122.9p per litre. In the same time Asda at Craven Way, Longwell Green, knocked 5p off unleaded petrol with its pump price now at 111.9p and diesel at 124.9p.

Sainsbury's at Bloomfield Road in Brislington and the Tesco on Eastgate Road in Eastville also have unleaded on sale at 111.9p and diesel at 124.9p.

Asda has challenged other major supermarkets to set prices nationally rather than locally, which it says will mean a better deal for drivers. Asda trading director David Miles said: “At Asda, you pay the same low fuel prices whether you're in Elgin or Eastbourne. The latest price cut is a further example of our commitment to make motoring more affordable for Britain's drivers.”

Tesco, Morrisons and Sainsbury's said they competitively price their fuel locally.

According to a fuel price comparison website, the maximum petrol price in Bristol at the moment is 123.9p for unleaded and 136.9p for diesel.

Hugh Bladon, a spokesman for the Association of British Drivers who is based in Weston-Super-Mare, said: “Although any drop in fuel prices is most welcome, they could come down a lot more if the Government lowered fuel tax. It is their duty to drop the level of fuel duty we pay.”

AA president Edmund King said: “The fuel price war started with the supermarkets last week and now we appear to be entering round two of the battle.

“Motorists have not had much good news this year, but the price reductions led by Asda will bring a sigh of relief. We hope that more retailers will join the crusade soon.”