Mrs Beckett has emphasised her left credentials, including the retention of her membership of the Campaign for Nuclear Disarmament, while claiming that she would be the most 'unifying' candidate in the mould of the late John Smith.
She has spoken of 'sweeping away' the Government's trade union legislation and of regaining public control of the water industry - pledges from which Tony Blair, the leadership favourite, has distanced himself. John Major seized the opportunity yesterday to dub her 'the striker's friend'.
She has distanced herself from the Blair 'modernising' drive by opposing party reforms until after the next election.
One MP who nominated her for the leadership claimed that Mrs Beckett had panicked when Mr Blair collected 154 leadership nominations from MPs. 'She's gone over the top, suddenly turning herself back into a real left-winger. It seems to me to be a terrible political mistake.'
The MP claimed the tactic would not help her gain many extra votes among the 4 million levy-paying trade union members.
Several MPs maintained that Mrs Beckett might well still beat John Prescott, the employment spokesman, to retain the deputy's post. 'There is no doubt that she's competent. She is more articulate than John Prescott. She can do joined-up sentences.'
Some MPs, including a number from the Blair camp, will support Mrs Beckett for the deputy leadership partly because they are opposed to the job going to Mr Prescott.
But there were warnings that, as in the past, the role could turn out to be one where the leader and deputy were 'at arm's length'. One Blair supporter said: 'If she pushes it too far she'll find it's a non-job.'
Mrs Beckett's supporters were angry at 'sniping' from the Blair camp. Dennis Skinner, the left-wing MP for Bolsover, said: 'They should come out of the woodwork and let us know who they are.'