Tory MPs have compared the panic over fuel supplies to the 1980s miners' strike and urged party members to "humiliate" the unions by stockpiling petrol, it has been reported.

In a private message from MPs to constituency associations, seen by the Daily Telegraph's Charles Moore, members were told: "This is our Thatcher moment."

The message reportedly continues: "In order to defeat the coming miners' strike, [Thatcher] stockpiled coal. When the strike came, she weathered it, and the Labour party, tarred by the strike, was humiliated. In order to defeat the coming fuel drivers' strike, we want supplies of petrol stockpiled. Then, if the strike comes, we will weather it, and Labour, in hock to the Unite union, will be blamed."

Labour immediately demanded an apology from the government.

Maria Eagle, the shadow transport secretary, said: "These allegations are outrageous. It is unacceptable that the Tory-led government have attempted to play politics with fuel supplies.

"People will be angry that David Cameron has inconvenienced millions in an attempt to create his own 'Thatcher moment'. The prime minister should apologise to the country for the chaos his government have created this week."

Number 10 described the claim as a matter for the Conservative party.

A Conservative party spokesman did not deny the existence of the memo and added: "The government has always been clear this is about doing everything possible to protect the country from a potentially crippling strike, and not about playing politics.

"We urge Unite to negotiate with the employers, and to make clear there will be no strike."

In his blog, Moore comments: "There is a key difference which ministers have not spotted. When Mrs Thatcher piled up the coal at power stations until the strike began in 1984, she was not inconveniencing the public.

"In 2012, the coalition is trying to press-gang the public, without saying so, into its political battles. All those people queuing on the forecourts were pawns in a government-organised blame-game."

He added: "No doubt many people reading this column are happy that Ed Miliband's and Ed Balls's dependence on a large trade union should be exposed, but very few, I suspect, appreciate being made into mugs. (And the political effect, of course, is the opposite of that intended: Unite now looks virtuous, and is much better placed to win its demands.)"

Len McCluskey, the general secretary of Unite, said the government's "posturing" was scuppering chances for an end to the tanker drivers' dispute, which has caused motorists to queues at petrol pumps across the UK and stockpile fuel in order to pre-empt any strike that could lead to a fuel shortage. "We call on the government to come clean on its whole approach to this dispute," said McCluskey. "Is it acting as an honest broker, or is it spoiling for a fight in order to get itself out of the political hole its class-focused economic mismanagement has put it in?

"Over the last few days its every move has been designed to whip up unnecessary tension at the expense of the public. Ministers knew all along that a strike could not possibly be less than seven days away even were it to be called – that is the law. Yet they panicked the nation all the way to the petrol pumps because they imagined it would boost them in the polls.

"The British people know that this posturing and positioning is poisoning the prospects for an early resolution to the dispute."

The government stands accused of mishandling the crisis by Labour MPs, who called for the resignation of Cabinet Office minister Francis Maude, who has faced a barrage of criticism from fire experts ever since advising motorists earlier this week to store jerry cans of fuel in their garages.

Calls for his resignation came after a woman suffered serious burns while transferring petrol into a jerry can in her kitchen.

The government has since changed its advice to motorists after Unite, the union representing 2,000 fuel tanker drivers, ruled out the threat of strikes over Easter. After days of urging motorists to fill up if their tanks dropped below two-thirds full, the Department for Energy and Climate Change said there was no need to queue on petrol forecourts.

"There is no urgency to top up your tank, a strike will not happen over Easter," it said.

But with Unite stressing it retained the right to call industrial action if talks, expected to start next week, break down, No 10 stressed the threat was not yet over. "It remains vital we take the necessary steps to keep the country safe in case there is a strike," a spokesman said.

The move followed more panic-buying at garages across the country on Friday, with petrol sales rising by almost 172% on Thursday and diesel sales up by 77%.

David Cameron said his heart went out to the woman in York who was burnt, describing it as a "desperate" incident.

Speaking at No 10 shortly after he chaired another meeting of the Cobra emergency contingencies committee, the prime minister welcomed Unite's decision and called on the union to engage constructively in talks expected to start next week at the conciliation service Acas.