Labour front-benchers are keen for the union to demonstrate its flexibility by offering to abide by any arbitration finding in the hope of preventing the dispute continuing into the autumn.
The search for a break in the deadlock has been prompted by a suspicion in some Labour quarters that the Government may be deliberately trying to prolong the dispute in the hope - so far unrealised - that public opinion will swing decisively against the strikers and behind the employers.
While supporting the RMT action, and the union's general secretary, Jimmy Knapp, shadow ministers are increasingly drawn to the idea that the union should seek arbitration as a means of securing a just and early settlement.
While the proposal for arbitration could be discussed between Tony Blair, the Labour leader, and TUC leaders when they meet tomorrow - the second day of the unions' annual congress - Mr Blair has so far refrained from intervening personally in the dispute because he believes political meddling by ministers has been a key factor in prolonging the dispute.
Traditionally, arbitration was the favoured method of settling disputes in the industry, but the Railways Staffs National Tribunal was finally abolished by the Government more than two years ago. The RMT has also, in private discussions, reacted negatively to the idea of arbitration, which could be set up under the auspices of the Advisory, Conciliation and Arbitration Service.
The Labour front-benchers who support a call for arbitration believe it would help sustain the high level of public support for the signal workers' action, and that it would damage Railtrack's image if it were to refuse a binding settlement by a third party. The immediate reaction from Railtrack sources last night was that they would not favour arbitration.
Union sources say Frank Dobson, Labour's transport spokesman, who has continued to be unequivocal in his support for the striking signalmen, informally approached Mr Knapp with a proposal for arbitration last week.
However, Mr Knapp reminded Mr Dobson that the signal workers' support for strike action was still solid, and said that the RMT was not prepared to accede to the intervention of an intermediary.
Mr Dobson was told that any worries about the political impact of the industrial action should be tempered with the knowledge that the public was relatively supportive of the employees' case.
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