Another of the leadership contenders, John Prescott, Labour's employment spokesman, became the first to implicitly back the industrial action by the rail workers.
Gordon Brown, the shadow Chancellor and close ally of Tony Blair, the 'modernising' favourite, was preparing to submit a nomination backing Mrs Beckett for the deputy leadership.
While Mr Blair's camp insisted that the shadow Home Secretary was 'scrupulously neutral' on the question of his deputy, Mr Brown's move will be taken as a sign that party modernisers would be happier if Mrs Beckett kept her former job as deputy leader rather than see it go to Mr Prescott.
As Mr Prescott declared that the necessary nominations for his leadership and deputy challenges were 'in the bag', Mr Livingstone conceded he would not attract enough support.
There was little doubt that Mrs Beckett would get sufficient backing for the deputy leadership contest when nominations close at 4pm today.
Mr Livingstone could have attracted the support of up to 20 of the 26-strong socialist Campaign group of MPs for the leadership, splitting the support of the left. He hopes that these will now back Mrs Beckett.
In the first declared constituency ballot, Leicester East Labour Party voted overwhelmingly for Mr Blair as new leader, Keith Vaz, the constituency MP, said. Support for Mr Blair was 69.6 per cent, with 21.34 per cent for Mr Prescott and 6.7 per cent for Mrs Beckett.
But the positions of Mr Prescott and Mrs Beckett were markedly reversed for the deputy leadership, with Mrs Beckett securing 68.5 per cent and Mr Prescott 30.3.
Mr Blair has attracted the public support of more than half the Parliamentary Labour Party.
David Hunt, Secretary of State for Employment, said the action by rail workers was 'a reminder of the politics of the past'.
Mr Prescott, however, told a Westminster news conference: 'I am sorry there's a strike. . . but I deplore the intervention of the Government. These are employees who have not been constantly in dispute. This Government has been preventing negotiation between the parties.'
Mr Livingstone's decision caused anger among some Campaign group members, who later decided not to back any candidate.
However, the maverick anti- Maastricht MP, Denzil Davies, indicated that he would continue fighting for nominations until the bitter end. The former Treasury minister and MP for Llanelli is not expected to attract more than a handful.
Another left-winger, Tony Benn, also weighed in with an accusation in the Tribune newspaper that the Shadow Cabinet was too negative.
The Commons Select Committee on employment will take evidence on the rail strike next month.
Leading article, page 17