At the east end, in the shadow of the statue of Wellington, a hardy band are braving the icy gusts which eddy round the plinth on which the Duke of Wellington is seated on his rearing horse, Copenhagen.
Their EU flags are being whipped into their faces as they attempt to hold them aloft, while a sign reading Beep to stop Brexit, is responded to by the occasional rush hour driver.
This is the Vigil for Europe. It has been meeting every Tuesday to Friday and Saturday afternoons for the last month and is just one of a many similar vigils being held across Scotland. From Inverness to Dumfries, Stirling to Skye, vigils have been springing up as people, many never previously politically active, have taken to the streets of their home towns and cities to protest against Brexit.
Morag Wilson, a part-time Napier University psychology lecturer, helps to co-ordinate the Edinburgh vigil. A member of the European Movement in Scotland (EMiS), she says the vigils are a grassroots movement, displaying a “regular, visible demonstration of public attitudes towards Brexit, in a nation which voted by a substantial majority to Remain in the EU.
“We’re here to give out information and to tell people that Brexit can be stopped. People tell us they feel powerless, that the UK government isn’t listening to them.”
The 68-year-old says she’s never demonstrated about anything political before. “The EMiS was set up just after WWII and the aim was to build better relationships across Europe with the desire to prevent a repeat of war.
“It’s always been about social and cultural exchanges, but that changed with Brexit. Now it’s a more political lobby group - not party political - but just determined to stop Brexit. The people who are here feel so strongly about this. The polls show more people would vote Remain now, people want this stopped - we’re here to show that is the case.”
Sally Macpherson is also retired, and says she’s joined the vigil and the Liberal Democrats after the EU referendum result. “I identify as a European and I don’t think anyone else has the right to take that away from me.”
Of course, not everyone who stops to talk agrees with the vigil. Fifty-year-old Paul Atkin is arguing the Leavers case. “We’ve had a People’s Vote - in fact we’ve had two if you count the original vote in the 1970s. These guys want a third vote to get the result they want - that’s not democratic. I voted Leave because I wanted our country to have control over itself - the EU and the Commission and the Parliament are undemocratic organisations.”
He moves on. Morag adds: “Most of the people who talk to us and take leaflets agree with what we’re saying, we get very few who are pro Brexit.
“But we’re here hoping to change their minds and to get MPs to stop this whole process.”