The chances of a second referendum are on the rise. Although the barriers to one actually happening remain considerable, that the prospects for Theresa May’s deal passing Parliament are so low means that all the other alternatives – including no deal – are becoming more likely.

Tony Blair gave an airing to an argument that some Remainers, and perhaps the official campaign, will seek to make in the next referendum whenever it happens: that the free movement of people can be reformed within the European Union. Some will talk about the existing powers to limit the right of movement that already exist, such as restricting access to social security, or deporting the long-term jobless to their country of origin, or through the introduction of ID cards. Others, as Blair did today, will hold out the possibility that the right of free movement might itself be curtailed, as the other 27 nations of the European Union have their own domestic concerns about migration to address as well.

There is a very important misconception here. Opposition to immigration on the continent isn’t driven by the free movement of European citizens within the bloc but the migration of people from outside it as part of the refugee crisis. Free movement remains one of the most popular parts of EU membership, commanding in support of more than two-thirds of people in every other EU country bar the United Kingdom. There’s an open question as to whether or not the ongoing refugee crisis is part of what drives concern over immigration here in the UK, but that is a conversation for another time.

What matters is that there is no serious prospect of any European politician being politically able to make changes to free movement. To give you an idea of the political implausibility of what Blair is suggesting: Romanian finance minister Eugen Teodorovici recently faced calls for his resignation after he suggested that Romanians should have their movement rights curtailed to prevent a brain drain in his country. (He subsequently apologised.)

Furthermore, as the number of immigrants – not just from within the European Union but from further afield as well – making use of the United Kingdom’s social security system is incredibly low, that “solution” cannot even be said to address the roots of voter concern about free movement: that is, the numbers of people who can freely come to the United Kingdom to live and work.

What some people advancing these claims will then say is, yes, there is no serious prospect of changes to free movement and that yes, the additional powers that the United Kingdom has opted not to use have no practical effect, but taken together the two can be used to “send a message” to people who voted Leave due to opposition to migration that their concerns have been heard and can be addressed even if we remain in the European Union.

There are a number of problems here, but the crucial ones as far as the politics of another referendum go are these: it isn’t true, and this will be pointed out, loudly, first by the various pro-Brexit campaigns but also by a number of Remainers. Most of the energetic and genuine grassroots pro-European campaigns that have sprung up since the referendum result are loudly and proudly pro-free movement and would drown out and debunk any anti-free movement message.

If you want to stay in the European Union, you have to win enduring popular support for the right of anyone in the bloc to move, work, and fall in love as they wish within the bloc. If you do not believe that a majority for free movement can be won in the United Kingdom, you have to accept that a second referendum cannot be won and that May’s deal is your only option to avoid a cliff-edge Brexit.