Downing Street has conceded that collective bargaining should be compulsory where more than half of any workforce are union members. Mr Blair has also agreed there should be no test of minimum union membership before a recognition ballot is held.
And while unions will be asked to accept a 40 per cent threshold for ballots for trade union recognition, it is understood that the figure may be left out of the main Bill and included in regulations to enable it to be reviewed after a reasonable period.
Senior ministerial sources said that could leave open the option of reducing the threshold to 35 per cent after a year, if a higher threshold proved unacceptable, without having to return to Parliament to amend primary legislation.
"If it is going to be under review, it will be in regulations. After a year you could change it to 35 per cent. That is being discussed," said one source. In a further compromise, there could be exemptions for firms employing fewer than 20 staff.
The CBI had wanted a 50 per cent threshold. But Labour MPs warned the Government at a meeting with Mr Monks at the Commons this week that there would be a big revolt if the Cabinet tried to impose a 40 per cent threshold without some sweeteners for the unions.
The compromise was thrashed out after John Prescott, the Deputy Prime Minister, angrily stepped in when it was reported that the 40 per cent threshold had been agreed. Mr Prescott's friends last night said the Deputy Prime Minister would back the compromise, if it won the support of the TUC.
The package was approved by the Cabinet after the draft White Paper "Fairness at Work" was outlined by Margaret Beckett, President of the Board of Trade. A senior source said the White Paper was likely to present the "pros and cons" of the 40 per cent figure.
The Deputy Prime Minister made it clear to Mr Blair that it was a "crunch" issue for him, and the deal appears to have reached approval from both sides. The Prime Minister's official spokesman said: "Every contribution endorsed the plan that Margaret Beckett outlined, including Mr Prescott."
While some sources emphasised the influence of Mr Prescott, others pointed to the patient diplomacy of John Monks, TUC general secretary.
While the CBI wanted to allow employers to define the "constituencies" for ballots on recognition, Mr Monks has successfully argued for a "neutral" system in which both sides attempt to agree, with recourse to an independent arbiter if that is not possible.
The TUC leader has also secured a compromise on the size of company to be excluded from the legislation. The CBI wanted organisations with fewer than 50 workers to be exempt, but that limit has come down to 20.
Mr Monks welcomed signs that the White Paper would be published next week and said that while some trade unionists would be concerned by the 40 per cent threshold, the White Paper should be judged as a whole.
Sources close to Mr Blair said the Prime Minister did not want a confrontation with the unions. "He wanted an amicable agreement and that is what we've got," said a source.
Mr Prescott insisted that final approval of the draft White Paper should not be given until next week, after agreement with Mr Monks. Talks are continuing, but it could be published next Thursday.