Asda and Tesco are reducing petrol and diesel prices by up to 2p a litre from today.
Asda, the first to announce a cut, said drivers would pay no more than 126.7p a litre for petrol and 133.7p a litre for diesel. It added its diesel would now fall to its lowest price since July 2012.
AA president Edmund King said: "Fuel price reductions at the pumps will bring a sigh of relief to many drivers who are struggling to make ends meet after bigger than normal financial outgoings during the festive period.
"We hope other supermarkets and fuel retailers follow the lead, otherwise we just end up with a fuel-price lottery based on proximity to certain supermarkets."
The other big supermarkets, Morrisons and Sainsbury's, have not announced their plans.