MR John Bruton and Mr John Major hope to clinch an agreement later this morning on, the procedures for the all party negotiations due to start in Belfast next Monday.
Hopes of a British Irish accord rose after more than four hours of talks in London last night between the Tanaiste, Mr Spring, and the Northern Ireland Secretary, Sir Patrick Mayhew.
Mr Spring and Sir Patrick confirmed that a number of issues would be referred overnight to the two heads of government. But Mr Spring said. "We have made very significant progress on a whole range of issues. I feel confident we haven made the progress we needed to today and can conclude matters very quickly."
The Taoiseach and the British Prime Minister are expected to hold a telephone conference later this morning, and Mr Spring and Sir Patrick hope to make a further statement in London this afternoon.
But it remains unclear whether the emerging agreement between London and Dublin on the key issues of decommissioning paramilitary weapons, and the chairmanships of the various strands of the talks process will be sufficient to secure an IRA ceasefire enabling Sinn Fein's participation in the process starting on June 10th.
Asked if he was hopeful the prospects for a ceasefire, one senior Irish source said "It might work more things are wrought by prayer."
But when Sir Patrick was asked if he envisaged talks about talks' or substantive negotiations, he replied as Mr David Trimble the Ulster Unionist leader, had stated on Monday that "the British government's position in that regard has not changed."
Last night's discussions were dominated by the issue of decommissioning and the search for agreement on the precise role to be played in the talks process by former senator George Mitchell.
It emerged yesterday that London, under pressure from Mrs Trimble, had been resisting Dublin's proposal that Mr Mitchell should chair the crucial Strand 2 North/South negotiations.
The Irish Times understands London's counter proposal was that Strand 2 should be chaired by the Canadian, Gen John de Chastelain.
And the indications are that Mr Major has secured Mr Trimble's agreement "in principle" that Senator Mitchell should be chairman of the overall plenary session of the process and also preside over the sub-committee which will address" the decommissioning issue.
The DUP leader, the Rev Ian Paisley, emerged from a meeting with Mr Major yesterday declaring that the Prime Minister had told him a "supremo chairman" would take charge of the plenary session, which would "have the final say and decision over all the strands".
Dr Paisley said that Senator Mitchell whom he described as "a crony of Gerry Adams" would chair the sub-committee on decommissioning.
But crucial to any London/Dublin agreement will be a convergence on the precise terms of reference for that committee to be appointed at next Monday's first plenary session and the question of a timetable for the implementation of whatever recommendations it might make.
Mr Trimble has agreed that discussions on decommissioning can proceed over a three month period until the end of September alongside consideration of the agenda and procedures to be followed in the negotiations.
But senior unionist sources last night again confirmed that they would not move into "substantive" negotiations until a timetable for decommissioning had been agreed.