Scotland Yard said it would now be contacting organisers of a wave of counter-protests in central London and Leeds, West Yorkshire, to inform them of the decision.
Anjem Choudary, leader of the radical Islamic sect Al Muhajiroun, said organisers Islam4UK had been forced to cancel the planned march from the House of Commons to Trafalgar Square because of security concerns.
But he added a meeting of supporters of sharia law would still take place at an undisclosed location.
A Scotland Yard spokesman said: "The MPS (Metropolitan Police Service) has been informed that today's planned march in central London has now been cancelled.
"Officers are now contacting organisers of planned counter protests to inform them."
The Islamic Society of Britain, which was planning to join other organisations in staging a "dignified, non-violent" counter-demonstration at Piccadilly Circus, said it would not now take place.
A spokesman said: "There's no protest so we won't be holding a counter-demonstration.
"It's a great success that pressure from all sections of the community, including Muslims, has resulted in the Muhajiroun and the hot-heads rethinking their position."
Source: Sunday Express