Among the companies likely to be excluded are British Gas, Scottish Power and Scottish Hydro. Also expected to be exempt from the levy, pounds 1.5bn of which Gordon Brown, the Shadow Chancellor, has pledged to job-creation and training schemes, are the small water companies, which supply 25 per cent of the market.
Other companies which have taken over utilities since privatisation are also arguing that they should escape the charge, as they have not benefited from the windfall that went to the original shareholders. Those that would fall into this category include foreign operators which have been snapping up the privatised electricity companies.
The prospect of Labour being forced to revise its plans to collect the pounds 3bn windfall tax, which has quietly been renamed as the one-off utilities monopoly levy, will embarrass the leadership, which tomorrow launches the "Road to Manifesto" policy document, as it will contain references to the levy.
Excluding some companies will not necessarily upset the overall aim of raising pounds 3bn, since the burden could be spread across the other companies caught in the net.
One analyst at Merrill Lynch, the City investment bank, pointed out that as the Labour Party had not released a formula for the tax, it was impossible to gauge how individual companies will be affected. It was possible, she said, for Mr Brown to raise his pounds 3bn, although his room for manoeuvre would be impaired.
Any softening of the stance towards British Gas is bound to provoke a hostile response from the left of the Labour Party, for whom the company is a symbol of "fat cat" capitalism. The exclusion of the two Scottish companies would lead to criticism that Labour is exhibiting one law for North of the Border and another for the South.
British Gas has argued that as it is the target of an aggressive pricing review from Ofgas, the industry regulator, which would hit its profits, it should not have to suffer a further onslaught from a new Labour government.
The Scottish companies have claimed that they were not sold as cheaply as their English and Welsh counterparts and have been subjected to a tighter regulatory regime.
A British Gas spokesman said yesterday that the issue of the windfall tax had been raised with the Labour front-bench: "There has been a process of discussion over the pricing review - it would be unrealistic if other subjects did not arise." He described the talks as "informal".
Scottish Hydro and Scottish Power have also been pressing their case for exemption. "Labour recognises the Scottish companies do have different backgrounds to the English ones," said a spokesman for Scottish Hydro. His company made profits last year of pounds 159m and Scottish Power made pounds 404m, but both feel they may avoid a windfall tax.
"It is nothing to do with benign fatherly treatment of the home country," said the Hydro executive, referring to the Scottish roots of many of Labour's Shadow Cabinet, "but to do with sound economic grounds."
The Scottish Hydro also claimed the English electricity companies were sold off more cheaply than their Scottish counterparts. Some of the English companies have seen their share prices soar from pounds 2.40 to pounds 10, while the Scots have gone from pounds 2.40 to pounds 3. "We are not making super-profits like the English utilities," said the Hydro official, "which is why Labour could well exempt us from the windfall tax." He added: "We have been making them aware of the situation."
Ian Russell, finance director of Scottish Power, was quoted recently in a local Scottish newspaper as saying: "Our judgment is that there will be a windfall tax but our base case on its impact on us, after discussions with Labour politicians, is conservative."
A utilities analyst at NatWest Securities said: "Scottish Power and Hydro believe they may be exempt." He added that "the market is assuming British Gas does not get hit". British Gas's current share price, he claimed, took account of its avoiding the windfall penalty.
John Battle, Labour's en-ergy spokesman, maintained that the tax would apply to all companies. "It is there for all utilities - that is what we've said and we're sticking with it."
A spokesman for Mr Brown was more circumspect. "It would be crazy if I said we will include or exclude anyone. In government we will talk about the situation. Until then, we will not say one way or the other," he said, adding that names of companies which may be excluded was "pure speculation".