They are moderates, support Everton football club and want to see a single united teaching union.

Brendan Barber, Trades Union Congress general secretary, and Steve Sinnott, the new general secretary of the National Union of Teachers, have a lot in common. They even both taught overseas.

Mr Barber, who helped broker the historic school workforce deal signed by all teacher unions but the NUT, goes as far as to describe their relationship as close.

And now he believes there is scope for bringing the NUT, Britain’s biggest classroom union, back into discussions with the Government and other unions.

He stops short of predicting that the NUT’s position on the deal will change, but Mr Barber is hopeful that the teacher unions can put the “rancour and antagonism” of the past behind them.

The TUC backs the deal, and the dispute between the NUT and the TUC-affiliated unions involved in it overshadowed the education section of last year’s conference. The NUT infuriated its “comrades” with spoiling tactics that included taking out a full-page newspaper advert and leafleting delegates.

The agreement does not feature as the main subject of any resolutions to next week’s TUCcongress which begins in Brighton on Monday, but more trouble is brewing. Unison, Britain’s biggest support staff union, was meeting yesterday to discuss whether it would remain within the deal.

Mr Barber believes the agreement is one of the best examples of social partnership, but that it would have been better if the NUT had signed up to it.

He said he had been closely involved in talking ministers into working with the unions. “There was a degree of persuasion to do.”

The NUT’s refusal to sign the agreement because it could open the way to assistants taking lessons has effectively frozen it out of talks with the Government.

Mr Sinnott said: “There is a difficulty in relations between the government and the NUT. Both sides will want to find a way forward. The appointment of the new general secretary creates an opportunity not just for the NUT but for the government to manoeuvre to end the difficulties.”

Mr Barber does not believe that the unions are compromised by the increasingly warm partnership with the Government which has followed the deal. Not everything in the garden is rosy. Mr Barber remains opposed to city academies (see opposite) because of the private sponsorship used to set them up, their potentially divisive nature and the possibility of more selection.

Then there are the private finance initiative schemes funding Britain’s new school buildings - “too much private involvement” and the evidence in their favour is “underwhelming to say the least”, he said. Mr Barber is also concerned about the idea of regional pay for teachers.

“The union voice is stronger than it has been for a long period, and the willingness of ministers to take account of well-founded arguments is much stronger than it was,” he said.

“There may always be major differences but it is unfair to suggest that the unions are merely nibbling away at the edges.”