The call came as the Rupert Murdoch-owned Sky News announced that it was joining the BBC in refusing to broadcast the Disasters Emergency Committee (DEC) appeal.
The broadcaster said in a statement that it had informed the DEC, an umbrella organisation for 13 humanitarian aid agencies, of its decision.
The decision comes after BBC director-general Mark Thompson defended the corporation’s decision not to broadcast the appeal in spite of more than 10,000 complaints.
He claimed that the BBC was “passionate” about defending its impartiality.
However, Stop the War Coalition spokesman Andrew Burgin pointed out that the fact that other channels including Channel 4, ITV and Channel 5 were showing the appeal showed how isolated and extreme the BBC was on this issue.
“Sky’s decision is just as disgraceful as the BBC‘s,” he said.
“Sky has a history of anti-union activity and its broadcasting headquarters will also be subject to protests later in the week.”
He added: “We are also asking local Stop the War groups outside London, which have a BBC office in their area, to organise similar licence return events, notifying the local media beforehand.”
Muslim youth organisation Ramadhan Foundation chief executive Mohammed Shafiq urged the BBC and Sky to reconsider their decision.
The BBC is also facing a growing revolt from its own journalists over its decision not to broadcast the aid appeal.
BBC staff have said that they have been told they face the sack if they speak out on the issue and corporation journalists will vote on Tuesday on a resolution put forward by the National Union of Journalists condemning the move.
The NUJ and fellow broadcasting union BECTU both passed motions over the weekend condemning the BBC‘s decision.
NUJ general secretary Jeremy Dear and his counterpart at BECTU Gerry Morrissey also sent a letter to BBC director-general Mark Thompson on Monday asking him to review it.