Bill Morris, the general secretary of the transport workers' union TGWU, said in an appeal to the black community: "It is inconceivable to support a government which has so often pandered to racism, most recently with the notorious Asylum and Immigration Bill."
But he told The Independent that the big issue that had to be addressed by all political parties - including Labour - was the opt-out from democracy, with an estimated 90 per cent of young black people not voting.
The Conservatives are nevertheless making a strong pitch for the Asian vote in the run-up to the next election.
Following his prolonged visit to the Indian subcontinent, John Major will on Saturday address a London rally to celebrate the 50th anniversary of Indian and Pakistani independence.
But Shamit Sagar, senior lecturer in politics at Queen Mary and Westfield College, London, and director of the ethnic minority side of the definitive British Election Studies, said Tory support was so low among the Asian and Afro-Caribbean communities that the Conservatives had "nothing to lose".
Mr Sagar said the Labour lead among Asian and the Afro-Caribbean communities was overwhelming. Aggregate figures collated by MORI for 1995 put Labour ahead by 80 per cent of the vote to 15 for the Conservatives, while the lead for the remaining ethnic minority community was even greater - with Labour ahead with 87 points to 8 for the Tories.
Mr Sagar was sceptical about suggestions that the ethnic minority vote could swing a number of marginal constituencies.
But a 1992 election study carried out by the Commission for Racial Equality said: "In at least three constituencies, a Conservative victory is attributable to ethnic-minority support.
"In Edmonton [north London], Ian Twinn had a majority of 593 and this study suggests that 718 voters from ethnic-minority electors were placed for the Conservatives. For Terry Dicks in Hayes and Harlington the figures were 53 and 410, while for John Watts in Slough they were 514 and 867."
Mr Sagar, who is preparing a 1997 election comparison of the voting behaviour of black and white voters - the first time such an exercise has been carried out - said there was no evidence that the ethnic minority vote could be mobilised to win or lose seats.
He described the suggestion that the ethnic minority vote could be used in that way as "a hollow threat".
As for the widespread view that Mr Major's visit to India, Bangladesh and Pakistan had to any degree been motivated by a push for the Asian vote, a Tory spokeswoman last night dismissed that as nonsense.
"I suppose," she said, "you will be saying that John Prescott's current visit to Hong Kong is a bid for the Chinese restaurant vote?"
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