Rishi Sunak has promised to consider another cut to fuel duty amid claims that prices at forecourts are “pump fiction” as they fail to reflect wholesale costs.

The chancellor said on Tuesday that he would examine whether to reduce the levy further after cutting it by 5p a litre in March.

Sunak is under pressure to help motorists paying record prices at the pump while the cost of other household goods has also jumped.

Petrol hit a new record average of 191.10p a litre on Monday, meaning it costs more than £105 to fill a 55-litre family car with petrol, up from about £72 a year ago. Diesel fell to 198.96p, just short of its high point set last Saturday.

A row is raging over who is responsible for the increase. Fuel prices were pushed up as oil soared after Russia invaded Ukraine, but wholesale costs have eased off in recent weeks amid increasing fears over a global recession.

Retailers have been accused of not passing on the 5p cut in fuel duty announced in Sunak’s spring statement to consumers. The Competition and Markets Authority (CMA) is investigating the matter and is due to report back to government on 7 July after a request by the business secretary, Kwasi Kwarteng.

The government has claimed that the reduction in fuel duty is equivalent to a £5bn tax cut. The Conservative MP Philip Davies asked Sunak in the Commons on Tuesday whether he would consider calls for a “more substantial” fuel duty cut, citing the temporary cut made in Germany until August.

Sunak responded that he would consider Davies’s recommendations. He said the existing tax cut was “significant, but we appreciate it is not being felt at the pumps because of the rise in wholesale prices. I want to reassure him that the energy secretary is in dialogue with the CMA to make sure that fuel duty cut is being passed on as well.”

The comments came after the AA said the government must step in to lower prices. Its president, Edmund King, said: “The pump prices are now more like ‘pump fiction’ as they don’t reflect the general downward trends we have been seeing in wholesale prices.

“This is now an urgent situation. The prime minister has hinted at action but we need more than hints. Pressure to force price transparency and a cut in duty would be a step in the right direction.”

The RAC fuel spokesperson, Simon Williams, said: “We strongly hope pump prices have peaked for the time being and will now start to decrease in line with wholesale prices which reduced last week. That, however, is the hands of retailers.”

Retailers have argued that they only make a few pence a litre, a weaker pound against the dollar is also pushing up costs and oil refineries are making greater margins than in previous years.

Separately, Kwarteng told MPs on the business, energy and industrial strategy select committee that the government is studying how to implement discounts to bills announced by Sunak last month.

The chancellor set out plans to dish out a £400 grant to cut bills over six months from October via energy companies. The plan raised questions over whether wealthy households and second homeowners would receive government help they do not need.

Kwarteng said: “My understanding is we’re looking at the delivery and how equitable that is.”

He said the support was a “much better structured form of intervention” than previous plans to knock £200 off energy bills that would be paid back over five years.