A new round of announcements on Twitter by the four main supermarket groups, saying they were cutting their petrol and diesel prices by up to 2 pence per litre (ppl), have received a cynical response from some consumers.

Sainsbury was the first to Tweet at 1.34am on Monday, followed by Asda three minutes later, Morrisons at 3.12am and Tesco at 4.32am.

Asda issued a press release saying customers would pay no more than 130.7ppl for unleaded and 134.7ppl for diesel at its 218 forecourts, and said it had acted immediately to pass on reductions in the wholesale fuel costs.

The supermarket group claimed it was the only one to have a national price cap, adding: “Prices at some other retailers vary by up to 6ppl depending on where you are.”

Andy Peake, Asda’s petrol trading director, said: “Our national price cap benefits everyone across the country, meaning that no-one filling up at Asda will be forced to pay a premium for their fuel because of where they live.”

However, one response to Sainsbury’s Tweet claimed the decrease “nearly offsets the rise you’ve done in the past couple of weeks”, a second pointed out the two Sainsbury’s near him had different prices, and a third said Sainsbury’s had recently increased prices in Rugby by 2ppl so it was just restoring the status quo.

A response to Asda’s Tweet said there was no petrol at its Newton Abbot store, while another said: “That just cancels the 2p increase a few weeks ago. I must have missed the tweets about that.”

Morrisons’ Tweet received no response, but Tesco received a volley of complaints about its fuel quality and one Tweet asking: “Why no flat national decrease.”