Anti-racism campaigners are due to stage a public rally ahead of BNP leader Nick Griffin's appearance on Question Time.
Unite Against Fascism (UAF) will hold the meeting as last-ditch efforts to stop Mr Griffin appearing on the BBC1 show continue.
Wales Secretary Peter Hain wrote to the BBC's governing Trust, appealing to it to reconsider its decision to allow the BNP to "the top table of UK politics".
He believes the party is currently illegal because it does not allow ethnic minorities to join.
Mr Hain appealed to the Trust as a last resort after BBC director general Mark Thompson rejected the Cabinet minister's arguments. He wrote that Mr Thompson "shows no willingness or ability to genuinely review his own decision" and was "too close to the decision".
Ex-army chiefs General Sir Mike Jackson and General Sir Richard Dannatt had earlier accused the BNP of "hijacking" military symbols for their own advantage.
Referring to their accusations, Mr Hain said "new factors need to be properly considered afresh in balancing freedom of speech versus protection of the vulnerable".
Mr Hain will also send a message of support to the UAF rally, which is being held in central London.
The rally will feature poet and former children's laureate Michael Rosen, director of the Anne Frank Trust Gillian Walnes and Reverend and the Makers frontman Jon McClure.
Mr Griffin sparked outrage by comparing the British generals to Nazi war criminals and claiming Winston Churchill would join the BNP if he was still alive. He also suggested his party was the most widely supported among rank-and-file soldiers.
