The poll for yesterday's BBC On the Record programme suggests Mr Blair is only modestly short of the 50 per cent he would need for outright victory without recourse to preferential second votes. And it also suggests that a challenge to Margaret Beckett as deputy leader would be unpopular - with nearly twice as many supporting her in the post as not.
In an assured and extended BBC interview yesterday, Mr Blair led a vigorous Opposition denunciation of John Major's attack on beggars and, in terms that may help to reassure union activists about his candidacy, declared that there was 'no incompatibility between decent minimum standards and fair treatment in the workplace and a society providing employment for people.'
Mr Blair said that it was in the interests not only of the unemployed but of 'all of us that we have a society where people can have work because we pay an enormous cost both economically and socially for very high levels of unemployment particularly when those levels of unemployment affect young people'.
Mr Brown, in an enthusiastically received speech to a European election rally in Luton, also attacked Mr Major's remarks on beggars and added that the Government should 'stop attacking the poor and unemployed and instead . . . start attacking poverty and unemployment'.
A number of senior Labour figures in both the unions and the parliamentary party - including Neil Kinnock, the former leader - are trying to find a way of breaking the impasse between Mr Brown and Mr Blair in a way that does justice to Mr Brown's acknowledged authority and support in the party while ensuring the two men work together for the continued modernisation of Labour in opposition and in power.
The new poll for the BBC's On the Record underlines that the decisive factor in the momentum for Mr Blair among individual party members is a belief that he is the best candidate to appeal to the floating voters that Labour needs to win over for a general election victory.
Of 472 randomly selected party members, 47 per cent preferred Mr Blair as leader - compared with 25 per cent for John Prescott and 11 per cent for Mr Brown. Eighty-seven per cent identified Mr Blair as the candidate who 'will appeal to floating voters' but only 42 per cent identified him as 'socialist'.
In the MPs and MEPs' section, among the 102 who took part, 38 per cent favoured Mr Blair, while Mr Brown was runner-up with 15 per cent.
Computing all three sections by using last week's NOP poll for the Independent and the BBC Newsnight programme, the corporation's Politicial Research Unit calculates that Mr Blair commands 48 per cent of the electoral college compared with 17 per cent for Mr Brown and 16 per cent for Robin Cook.
Mr Cook, Labour's Trade and Industry spokesman, in an interview interpreted by some colleagues as indicating he may be preparing to withdraw from the contest, told On the Record that 'Whoever the Prime Minister is in No 10 I shall be very happy to work in the team that is delivering those policies.'
Asked specifically whether he was ruling himself out, Mr Cook replied: 'No, I think that can wait till another interview.' But although his friends dismissed such an interpretaion yesterday, one Shadow Cabinet member said last night: 'It sounds as if the Cook plane is preparing to land.'
Whether or not Mr Cook runs, Mr Prescott remains a potential candidate for both the leadership, and, possibly for the No 2 job as well, especially if Mrs Beckett ignores her support as deputy and runs for leader.
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