A joint statement by 44 people accuses the party, which is contesting Lewisham’s mayoral election, of stirring up race hate.
Along with other mayoral candidates, signatories also include the Bishop of Woolwich the Rt Rev Christopher Chessun and Archdeacon of Lewisham Christine Hardman.
Representatives from Unison, the National Union of Teachers and students’ unions have also signed.
The statement says: "As representatives of many political opinions and parties in Lewisham, we affirm the values of unity, tolerance and mutual respect, which have always helped people from different backgrounds to live together.
"We are deeply concerned at the activity of racist and fascist groups such as the British National Party, which use people’s fears to stir up race hate, which their candidacy in the Lewisham mayoral election will seek to do.
"We also reject their demonisation of Muslims, and their claim to speak for Christians, as an affront to all our religions and beliefs and a danger to the unity of the whole community.
"In the next few months the people of Lewisham will choose their mayor who will lead Lewisham Council in all its policies at the town hall.
"We believe that a high turnout of voters will minimise the impact of candidates on extremist platforms in our borough.
"So we urge the overwhelming majority to turn out and vote, and give a clear signal that messages of race hatred and division are not welcome here."
Chairman of the Lewisham Anti-Racist Action group Councillor Jarman Parmar, who organised the statement, said: "Fascists were stopped in Cable Street in 1936 and at Lewisham in 1977, by myself and many others. They must be stopped today."
Tess Culnane, who has previously run for the National Front and has spoken at a meeting of the far-right British People’s Party, is standing as the BNP candidate.
News Shopper is awaiting a comment from Ms Culnane.
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