A litre of unleaded has fallen by 1p to 105.9p and diesel by 2p to 116.9p at Asda's 170-plus petrol stations across the UK.
Morrisons is to follow suit with similar cuts, although its fuel will remain more expensive at 106.6p and 117p.
Latest UK average prices are 109.89 for unleaded and 121.54 for diesel.
AA spokesman Luke Bosdet said: "Although very welcome in bringing the cost of a tank of petrol down by 50p, many non-Asda towns will still be charging 3p a litre more next week.
"This turns buying fuel in the UK into a postcode lottery where drivers in one town can be spending £1.50 a tank more than another just down the road.
"Drivers are rightly angry about this and many have complained to their local MPs."
Asda trading director Darren Blackhurst said: "We review our fuel prices daily and are committed to passing back the benefits of lower cost prices to all our customers with our national price.
"We urge our rivals not to take advantage of drivers who don't live close to an Asda petrol station and to pass on cost benefits fairly to all their customers."
© The Press Association 2008