Does the mass march make a 'People's Vote' more likely?

It is a fact of our political system that you cannot vote with your feet.

And so arguments over the precise size of the crowd that marched through London today demanding a "People's Vote" are largely irrelevant.

There was no threshold that the number of marchers could have passed which would trigger a second referendum - whether it was 700 people or, as organisers estimate, 700,000.

That's not to say protests do not matter - it was a major expression of public opposition to the government's current trajectory; there were certainly hundreds of thousands of people; and it was certainly one of the largest demonstrations the capital has seen since the anti-war march of 2003.

But back then Tony Blair was able to ignore the passion of the million or so anti-Iraq War protesters because he had a majority - and backing from a number of opposition MPs - that would see any decision to go to war in Iraq get through parliament.

Theresa May does not have anything like a safe majority, but what she does have is a legal process, in the form of Article 50, which means she can theoretically ignore the people's vote demands.

If she can get a deal with the EU, and get that deal passed by a majority of MPs, the UK will leave the EU next year with no requirement for her to grant a second referendum on the terms - no amount of street protests can change that fact.

The problem for Theresa May, however, is that it remains far from clear whether a deal on the Withdrawal Agreement with the EU is possible, and even more uncertain whether a deal that the EU are content to sign is one that MPs will accept.

Indeed the prospect of complete gridlock in parliament is very real - with no majority for a no-deal exit from the EU, and major question marks over whether there is a majority for the kind of deal Mrs May is hoping for.

With the DUP and the ERG wing of hard Brexiteers in her own party seemingly dead set against what the government is trying to negotiate, it would require a significant number of Labour MPs to defy their own party and support Mrs May.

While a clutch from certain leave-voting constituencies might do this, it is unlikely to be enough.

It is this prospect of impending parliamentary paralysis that increases the plausibility of a further referendum as an option.

Arguments that the 2016 vote was illegitimate because voters were misinformed by the campaigns will likely continue, so too will those that say people should have a say on the final details of a deal because these weren't known in the first vote.

But so long as she can secure a deal, Theresa May can continue to shrug these off.

If, however, parliament gets to the point where a firm decision is impossible, the argument that a second referendum could be used to end the impasse is likely to be harder to dismiss.

Labour, of course, say they want a general election in these circumstances. But that is not something the government is obliged to offer due to the Fixed Terms Parliament Act.

There are all sorts of issues that a second referendum would create - from what options are on the ballot paper, to the question of timing and whether article 50 process would need to be extended, to what happens in practical terms if the people's vote returns a second majority for leaving the EU.

That said, it is not totally implausible that enough Tory MPs could conclude they would rather deal with those issues than fight a general election which could put Jeremy Corbyn in Downing Street.

We are not there yet, and despite the massive turnout at the march, it is still the case that you cannot vote with your feet, no matter how many walk together.

But you can send a message. And today that message will have been heard loud and clear, not just by the prime minister, but by Jeremy Corbyn - if a second referendum is to happen, one of them will need to back it.