So far no less than five lobby groups, including The National Assembly Against Racism, have joined the protest, which is being run through Black Information Link (Blink).
They argue the programme, due to be broadcast on August 26, is likely to incite racial violence and boost support for the British National Party.
Visitors to the Blink website can send a protest email by simply clicking on the name of Andy Duncan, the chief executive of Channel 4.
Tessa Jowell, the culture secretary, also appears on the site and is expected to be bombarded by emails.
The documentary caused a furore when it was pulled from Channel 4's schedule in May. The BNP had posted an article on its website claiming the programme was a "party political broadcast".
Peter Dale, the head of documentaries at Channel 4, said: "This is an important, well-researched and produced documentary. We believe it is a fascinating insight into the work of the social services in Bradford, crafted in a fair and measured way, and it is in the public interest that this film be shown."
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