He called for a cut in union places on the party's National Executive, as a survey found that half of Labour MPs want to end their union sponsorships.
In a move which will dismay union leaders and many in the party, including the deputy leader, John Prescott, Mr Straw said on BBC Television: "The time has come for the National Executive Committee to be reformed. At the moment it is composed only of people elected by the trade unions and the constituency parties and those of us who are described as constituency representatives are on the whole senior parliamentary politicians. There is a strong case in addition for true representatives of constituency parties and representatives of local government. I hope over the next two or three years we can agree changes without a row."
The momentum for change was strengthened by a survey of 120 Labour MPs in the Observer newspaper, which found that 57 of them thought that union sponsorship of MPs should be ended, while 55 wanted to keep the system.