Forget the spat with the RMT. That's small fry. There's a much bigger battle going on between the Labour government and the trade unions. In Downing Street, they're furious. They're calling it blackmail.

"We're not talking small, far-left unions, we're talking the big three," says one senior official. "They're trying to hold us to ransom."

Officials close to the Prime Minister estimate that, in the 12 months since the last general election, union contributions to the Labour Party have fallen by £1.5m. For a party heavily in debt and struggling to entice rich donors to bail it out, the shortfall is potentially devastating.

Union and government sources agree on the provisional figures and on the reasons behind them. A clever game is going on. The three biggest unions - the T&G, GMB and Unison - have held back payments in direct retaliation over government policy. They've done this by roughly equal amounts, ensuring that each union's share of the block vote at the Labour conference, which is determined by the size of the political levy, won't go down. Smaller unions have followed suit.

Downing Street's anger is directed mainly at John Edmonds, the GMB leader, who is regarded as the ringleader. He is accused, variously, of arrogance, grandstanding and of being a "pillock".

What has particularly riled the government is that, on 24 June, Edmonds drank white wine in the garden of No 10 at a union reception hosted by Tony Blair and an array of cabinet ministers. Then, the following day, he took to the airwaves to denounce Blair and proclaim that he would prefer to do business with Gordon Brown.

"The other unions leaders have a go at us on policy. That's their right. We respect that," says one government official. "With Edmonds, it's personal. He thinks he could do a better job of running the country than we can."

The running sore since the election has been the government's plans for private-sector involvement in public services. Bill Morris, the T&G leader, has spoken out vociferously against David Blunkett's asylum and immigration curbs. Employment law has, in the view of the unions, improved only marginally. When John Monks, the TUC general secretary, attacked Blair's links with Silvio Berlusconi as "bloody stupid", it was regarded as one of the most popular things he's done.

The fracas with Edmonds is seen as a symptom of a wider problem. The view at the TUC and at various union headquarters is that relations with the government are particularly difficult.

But as one union source put it, "they've not been easy at any time since 1997". Day-to-day contacts have not been helped, the unions say, by the loss of Jon Cruddas, Blair's union fixer in the No 10 political office who became MP for Dagenham at the last election; and Ian McCartney, who at the Cabinet Office kept his eye on the union link but who last year was given the poisoned chalice of pensions.

The RMT action last week was brazen - making sponsorship of MPs contingent on their support for union policies such as opposition to public/private partnerships.

"We don't deal in politics by reward," says one senior cabinet member. But Cruddas, who knows the relationship better than just about anyone, believes the RMT's actions are consistent with the approach of the union movement in general. He points to a long-term trend of unions cutting their automatic levy to Labour and keeping back more money for their "discretionary funds". This they have been using for their own campaigns. At the same time, the unions are being more up-front about linking their financial support for Labour with their approval of government policy. They turn the tap on. They turn it off.

At the moment, the cash is only trickling in. The total for January-March 2002 showed a paltry £850,000 overall from the unions. The GMB and Unison gave little over £10,000 each. The total from the unions since June 2001 is £4.5m - the party had been expecting around £6m.

But for all the grandstanding, will the unions do the necessary thing for the party at the next election? In the past, they always have, no matter how bad relations have been. One senior union official believes they will: "If we thought the government was under a serious threat from the Conser-vatives, we would be making our points in other ways." Others are not so sure.

On both sides - party and unions - talk of breaking the link is no longer a taboo. The Institute for Public Policy Research is conducting a study on the future of funding, which will examine the financial stranglehold the union movement has on Labour. For change to happen, Blair will have to be persuaded to embrace state funding. He is said by officials to be "still unpersuaded, but, for the first time, persuadable".