The fuel price cuts claimed by supermarkets earlier this week have been patchy, and in many cases below the 2ppl headline figure, according to the AA, which says non-supermarket retailers are undercutting superstores in some locations.

Commenting on the latest AA Fuel Price Report, it said: “The true meaning of an ‘up to 2p’ cut in pump prices is mainly a 1ppl reduction, except for Asda. It also shows that some non-supermarket retailers were still undercutting the superstores on Wednesday – despite the price ‘skirmish’.”

It added: “The Big Four’s generosity has been far from consistent around the country.”

Last month, the AA said that supermarkets had “lost the plot on pump prices”. The gap between them and non-supermarket retailers had narrowed to its closest in a year and independents were starting to undercut the superstores.

Today, it said: “With Tuesday’s pump price cuts, supermarkets were still not all on the same page.

“Sainsbury’s has made the biggest cut since last month but, coming from a higher starting point, still averages at least 2ppl more expensive than Asda and Morrisons - as does Tesco.”

Using the AA App’s fuel price search, it said that, even with Tuesday’s pump price reductions, the cost of supermarket petrol can vary by nearly 7ppl along some routes.

Despite the claimed price cuts, the average UK pump price of petrol had fallen from 120.07ppl over the weekend to 119.31ppl on Wednesday, the day after supermarket price cuts were due to take effect.

Petrol’s average pump price peaked at 120.45ppl on 19 February before beginning to slip lower. This ended a nearly three-month period of rising prices, which started on 28 November with petrol at 113.89ppl.

On Wednesday, the average price of diesel was down to 121.44ppl, having been 122.04ppl over the weekend and at a peak of 122.35ppl on 20 February. This too had come off the back of a steady rise since late November, when diesel typically cost 116.29ppl.

Edmund King, the AA’s president, commented: “The cut in supermarket pump prices is very welcome, particularly after the 6.5ppl or £3.50-a-tank surge in petrol costs since late November. Asda’s 2ppl cut was bold when taking into account recent oil price and exchange rate volatility, which can explain why other supermarkets’ price reductions have been more muted.

“However, from a driver’s point of view, living in the wrong town with an uncompetitive supermarket can be costly. The AA’s price search tool shows that there are still non-supermarket retailers prepared to step in with lower prices when the local superstore drags its feet when passing on cuts in wholesale costs.

“We expect that the fall in wholesale costs, providing it continues, will see bigger price cuts become more widespread. But, it still leaves the impression that many retailers are ‘feathering’ potential price falls.”