Mr Bickerstaffe is to reveal his intentions today at a meeting of the Unison executive because he wants more time with his family and on other pursuits.
He never knew his father, but recently discovered relatives in Ireland, including three half-brothers.
He is also known to have grave misgivings about New Labour and its strategy for bringing in private companies to run public services.
Mr Bickerstaffe has been a doughty champion of the low-paid and fought long and hard for a national minimum wage. He believes the present pounds 3.60 an hour is too low, but has always been measured in his criticism of the Government.
After the Prime Minister said last week he "bore the scars" of his attempts to promote change in the state sector, Mr Bickerstaffe said many of his members bore the scars of low pay. He suggested Tony Blair had been "tired" when he made his unscripted remark.
Mr Bickerstaffe is known to favour Dave Prentis, 49, his little-known deputy, as the best candidate for the leadership.
Mr Prentis, very much the favourite to take over, is known as a hard- headed negotiator and a "moderniser" who has pushed through reforms to Unison's internal structure.
He has fewer links with Labour than Mr Bickerstaffe, and sources in the union believe his politics are not dissimilar to that of his senior colleague. But New Labour will be hoping he will be more amenable to change in the public sector.
Mr Prentis was a national official with Nalgo, the white-collar town hall union, not affiliated to the Labour Party,which merged with the National Union of Public Employees and the health union Cohse to form Unison. Mr Bickerstaffe was general secretary of Nupe, a left-led organisation with strong links to the party.
The son of a nurse, the present leader has strong working- class roots in Yorkshire and came to prominence as a Nupe official in the 1979 "winter of discontent", when one group ofunion members refused to bury the dead as part of their industrial action over pay.
Mr Bickerstaffe took over as general secretary of Unison on 1 March 1995 and his period of office ends officially in 18 months. He is expected to go several months early. The election for his successor will be next summer.
He earns around pounds 60,000 but still lives in a modest house in south-east London.
When he became general secretary he suggested that a woman was appropriate for the job because the union had high female membership. But no woman has since reached a senior post within the union.Reuse content