It is being hailed as the most important speech of her career, but actually, as Theresa May makes her speech from the City that made Michelangelo famous, her real target is the electorate at home, and maybe even more than that , her own political party.

Jonathan Portes, economics professor at Kings College, London, and one of the leading experts on Brexit – although to be fair, it should be pointed out that he was vehemently pro-remain, so he may not be the most objective – said that Mrs May's speech represents a key moment in her negotiations – negotiations with the rest of her cabinet.

The EU’s position has not changed, it is the same now as it was when Mrs May talked about Brexit meaning Brexit, about how she wanted a red, white and blue Brexit. Mr Barnier, the EU’s chief negotiator confirmed this the other day, saying: “I would like to be very clear: if we are to extend for a limited period the acquis of the EU, with all its benefits, then logically ‘this would require existing Union regulatory, budgetary, supervisory, judiciary and enforcement instruments and structures to apply’ – as recalled in the mandate I received from the European Council, under the authority of President Donald Tusk.”

This position has never changed, it is something that too many in the Brexiteer camp still don’t get. To the grandees in Europe, there is more to the EU than free trade, it is a club, designed to permanently cement economic, political, social and diplomatic unison in a region that has been riven by war for as long as history can recall.

The UK focuses on trade, and economic expediency, but to the likes of Jean-Claude Junker, and indeed to Emmanuel Macron and Angela Merkel, there is more to it than that, so much more. The Brits may be known within the EU for their pragmatism, but to others there is ideology too, and break that ideology, and the EU is nothing, if the EU is nothing, Europe returns to chaos – that is the narrative within the EU.

Mr Barnier also said: “One thing is sure: it is not – and will not – be possible for a third country to have the same benefits as the Norwegian model but the limited obligations of the Canadian model.” The UK seem to think that because of its economic clout, it can have both. But if that was the case, what is the point of the EU? And that is a question no one within the EU wants to see asked.

Mrs May is now pushing for a two year transition period, something that her chancellor Philip Hamond was calling for some time ago. In the deal that Mrs May is hoping for, the UK forks out 20 billion euros. That fee is slightly less than what the UK normally pays into the EU, but this is justified as during this two year period, the UK would have no say over the EU’s decision making. So it is argued, it is only right that the UK pays a little less.

But unless this two year period allows for free movement of labour, and the granting of full rights to all EU citizens living in the UK during this period and to be extended indefinitely, there will be no deal. And the EU will surely require further compensation, beyond the 20 billion euros.

In the world of libertarians, if you have decided you have had enough of your partner, you say: “you are dumped” and that is it. A ‘nice’ libertarian might say ”you can sleep on the sofa for a while, while you sort yourself out.”

But, the real world is not like that, divorces are complex, and both parties are rarely satisfied with how a court decides how to divide the spoils of a dissolving partnership. Indeed, the perfect divorce is normally one in which both parties feel mildly aggrieved. The trick is to find the point when the level of aggrievement on both sides is about the same.

Yanis Varoufakis, the former Greek finance minister, has argued that the UK should opt for a five year transition deal, in which the UK remains part of the EU in all respects but name, so that is five years of contributions to the EU budget, five years of free movement of people. By doing this, Michel Barnier is made irrelevant, there is no need for negotiations.

The UK then has five years, post legally leaving the EU, to agree trade deals around the world, and agree on a settlement with the EU. Such a deal may be unpopular with the 52 per cent who voted Leave, but neither will the 48 per cent who voted Remain be happy – many are still clinging to the hope that the Brexit vote will be overturned.

And since the arrangement recommended by Mr Varoufakis would be unpopular with both the Remain and Leave sides, it is probably the right one.

Florence is a beautiful city, and it is one that during the Renaissance became hugely prosperous on the back of commerce. That is why Mrs May chose to make her speech in this city.

But will there be room for a view of an EU and UK can that finally understand each other’s position?