Comparisons have been drawn between the 700,000 strong Peoples Vote march on Saturday and the 1,000,000 who turned out to protest against the war in Iraq in 2003.

The numbers for both events are obviously huge but the question is do demonstrations of this sort actually achieve anything? After all, the war in Iraq went ahead with some terrible consequences for the region and Tony Blair still went on to win a third decisive election victory in 2005.

If the two individuals who could do most to deliver a People’s Vote – the PM and the Leader of Her Majesty’s Opposition – were both conspicuous by their absence, then why should the demonstration change the course of Brexit. We’ve had a vote, Brexiteers say, and the people voted to leave.

But demonstrations of this size and nature do matter. They are often totemic of a feeling that public opinion has got ahead of the politicians; marking a wider cultural shift in ways that are not always immediately obvious.

In 1961 CND’s Aldermaston march came on the heels of Suez and Britain’s loss of status as a major military power. It signaled the end of the age of deference which culminated in students fighting with police outside the US embassy before the end of the decade.

Famously, the 1990 Poll Tax demonstration saw wide spread rioting in Trafalgar Square and the removal of the seemingly unassailable Margaret Thatcher within weeks.

The Stop the War coalition didn’t change foreign policy, but it did reset the narrative which led to Tony Blair being viewed, not as Labour’s most successful ever politician, but to being discredited as a liar and war criminal by his own party and paving the way for Jeremy Corbyn.

In many ways Saturday’s demonstration is a game changer. 700,000 politically engaged people on the streets, without a single arrest or sign of trouble, is a big number. It represents a very polite uprising of the progressive centre, many of whom carried placards saying, “I gave up a bottomless brunch for this” and “I’m very cross”. It was even likened by some as being the longest ever Waitrose queue.

The Guardian pointed out that Saturday’s march was larger than the memberships of both Labour and the Conservatives combined. This is quite something given that Labour likes to brand itself as a mass movement. Many on the march will have been Labour and Conservative members who are at odds with their leaders.

Currently the approach of both parties has being shaped by a relatively small coterie of politicians who want Brexit but for ideologically different reasons and who strain against the grain of their parliamentary parties. As they pull in opposite directions they are creating space in the middle for a wider public view which is now finding its voice and has some wind in its sails.

When Chinese Premier, Zhou Enlai, was asked in 1972, what he thought about the impact of the French Revolution, which had taken place 200 years earlier, he replied that it’s “too early to say”.

While it might be too soon to understand the exact ramifications of Saturday’s march what’s certain is that something important has happened. Regicide apart, the next scheduled general election is 2022, by which time Theresa May will have departed and a 73 year old Jeremy Corbyn will be seven years into his leadership – the traditional point when voters get bored.

It’s likely then that the next generation of political leaders will look a bit more like the queue at Waitrose and a little less like the angry ideologues, on both left and right… A little less take back control and a bit more about life’s essentials.

This will require a policy shift in terms of funding for social care, industrial strategy and wage stagnation, immigration and house building, designed to addresses the reasons why people voted to leave in the first place. And this, perhaps, more than the wording on the ballot paper of a people’s vote, will be the true legacy of Saturday’s march.