Tax cuts for ordinary families should be funded through a windfall tax on oil companies, Derek Simpson, the joint general secretary of Unite said today.
In an interview with the Financial Times, Mr Simpson said Labour could win back support by adopting the measure.
"How popular do you think it would be, given that oil companies are raking in billions, if he imposed a windfall tax on them and distributed it through something like a council tax cut?", he said.
In a later interview on Radio 4's Today seminar, he continued: "The first thing is to try to convince those core Labour voters that appear to be deserting in droves that the Labour party is on their side and is pushing for their interests, rather than the interests of others.
"People are very concerned currently about the high price of fuel and the rising cost of food, the lack of affordable housing, and there is still a residual concern about pensions in the future and job security.
"These issues need to be pushed and measures need to be put in place that would secure people's concerns."
Such a policy would not be without precedent. The New Deal programme was funded by a one-off windfall on utility companies shortly after the party came to power in 1997.
Mr Simpson poured cold water on rumours Unite would withdraw funding from the party.
"You only need to examine what the last Conservative government did to trade unions and to the working people that they represent to understand that merely deserting Labour and losing faith is not the answer, because it leads to a Conservative government, which is certainly not in the interests of the vast majority of British people," he said.
"The answer lies in trying to find a new direction that can reconnect. I have to be concerned because of the disillusionment that many members have, but I try to argue that changing the funding is ridiculous.
"Simply defeating the Labour party through lack of finance leads to a Conservative government and any right-minded working person would understand that a Conservative government - despite their apparent sheep's clothing at the moment - is not in the interests of working people."