Keir Starmer will on Monday announce tens of millions of pounds’ worth of support for Britons hit by a spike in energy prices as a result of the Iran war.

The prime minister will lay out the plans during a press conference in Downing Street on Monday, during which he will also take aim at some suppliers of heating oil for price gouging.

The support package is understood mainly to be targeted at people who use heating oil to warm their homes, many of whom live in rural areas of Northern Ireland where the prime minister visited last week.

Starmer will say: “It’s moments like this that tell you what a government is about.

“My answer is clear. Whatever challenges lie ahead, this government will always support working people. That is my first instinct – my first priority – to help you with the cost of living through this crisis.”

Oil prices have jumped in recent days as a result of the effective closure of the strait of Hormuz, through which much of the world’s oil supply passes.

The impact is being felt both at petrol forecourts and in the estimated 1.7m UK households that use heating oil, which are not covered by Ofgem’s energy price cap.

The Guardian revealed last week that ministers would provide help to those in England via councils using the new crisis and resilience fund, while devolved governments in Scotland, Wales and Northern Ireland will receive money to deliver the help.

As well as announcing the extra support, Starmer will criticise suppliers of heating oil, after the competition regulator warned there was evidence that deliveries that had already been agreed were being cancelled or renegotiated.

The Competition and Markets Authority has begun a review into the sector and has written to suppliers, asking them for more information about their contracts.

Starmer will say on Monday: “I will not tolerate companies trying to exploit this crisis to make money from working people … If the companies have broken the law, there will be legal action.”

Ministers are also not ruling out the possibility of cancelling a planned fuel duty rise in September.

Asked on Sunday whether that rise would still go ahead, the energy secretary, Ed Miliband, told the BBC: “We will stand by the British people in this crisis, and we’ll do what it takes to do that.”