Far-right campaigners had hoped to march down the High Street to the Scottish Parliament on Saturday, 23 August.
However, following an objection from Police Scotland, Edinburgh city council licensing committee yesterday vetoed the demonstration.
The move comes less than 24 hours after councillors gave the go-ahead to a 15,000-strong Orange Order parade in the city on 13 September, five days before the independence referendum.
SDL organiser Graham Walker said: “The Orange Order is allowed to march after all the trouble and a girl getting bottled at their recent march in Glasgow, plus the James Connolly Society and the United Against Fascism were allowed to march in the city earlier in the year.
“Yet we are the ones who are picked on and blamed for causing public distress.”
Police Scotland superintendent Phil O’Kane told committee members there had been six SDL events in Edinburgh over the past four years and that four of them had been well organised, with “no significant public order issues”.
He then told how the force’s decision to object to the event stemmed from the arrest of four SDL members at a counter protest to the Celtic Commemorative Committee’s march in May this year which had led to concerns that organisers could no longer exert control over their members.
Mr Walker disputed the police’s claim and told the licensing committee meeting those arrested had not been SDL supporters and that the counter protest was not an officially organised demonstration by the SDL.
Edinburgh’s city community safety manager Andrew Mitchell told the meeting: “If approved, we would expect a submission for a large counter demonstration to be lodged pretty much straight away.”
In ruling against the SDL parade, committee vice-convener Councillor Elaine Aitken said: “This march is prohibited on the grounds that Police Scotland feel you cannot ensure your members will comply with police direction.”
Mr Walker later told The Scotsman he felt the decision had been a “political decision from the higher-ups at Police Scotland”.
He said the SDL intended to hold a static demonstration outside the Scottish Parliament on the day despite the ruling.