The society, funded by both sides of industry, will warn against Mr Blair's strategy of erecting substantial barriers in the way of union recognition - a position endorsed by media tycoon Rupert Murdoch.
The statement from the society is due be issued today as a group of Labour MPs meet Margaret Beckett, President of the Board of Trade, to express concern over signs that Mr Blair may be bowing to the demands of Mr Murdoch and other employers.
In particular, the society is concerned about the Prime Minister's interpretation of a clause in the manifesto which says that union recognition should be granted where a ballot of "the relevant workforce" produces a majority.
Mr Blair is understood to favour an argument advanced by the Confederation of British Industry which would insist that recognition could only be granted if a majority of the entire workforce eligible to vote supported it, rather than a simple majority of those voting.
John Knell, head of research at the Industrial Society, acknowledged yesterday there had been considerable debate on the issue, but "the argument that a ballot would be deemed successful if a simple majority of votes are cast in favour, remains compelling, particularly if balanced with a meaningful participation threshold".
The society is understood to be unhappy with a "fallback" position being floated by Labour sources, which would set a threshold for participation in a ballot as high as 80 or 90 per cent.
The Industrial Society's intervention comes after a letter to Labour MPs from the Trades Union Congress which told them that if they had stood for election under the CBI system, all but 14 would never have reached the Commons.
The society is less supportive of the union line on how the voting "constituencies" should be drawn up. Mr Knell points out that this is a crucial issue in determining how the law will operate. He says that the "more straightforward and workable the definition the better". The society is understood to favour the CBI position on this issue, which means employers will be able to decided the boundaries based on company structures. The TUC position is thought to be too complicated. Unions fear that companies will "gerrymander" the constituencies to minimise the likelihood of recognition.
Union leaders are due to meet Mrs Beckett early next week to urge her to honour the manifesto on union recognition. It is thought that they will be pushing at an open door. The real difficulty will be to persuade Mr Blair.
A White Paper on employees' rights, which will contain recognition proposals, was due last autumn, postponed until this month, and since delayed until March or April.
Mr Murdoch's position was made clear yesterday in a Times leader arguing that "easy union recognition could bring back the bad old days". He fears that the GPMU print union could win representation rights at his Wapping plant. His newspaper titles were transferred to the complex in east London in1986 after 5,000 employees were dismissed for going on strike.