The Tories are in a mess on Brexit. The nation remains divided. But everyone accepts the need to prioritise reducing immigration, even at the expense of lower living standards.

These are the three key truisms of post-referendum Britain. But it turns out that only the first of those two propositions is actually true. The third, that there is a popular will to lower immigration at almost any cost, is not true at all. The latest poll from YouGov shows that even a majority of Leave voters are unwilling to accept any reduction in their living standards at all in order to curb immigration.

In the era of "fake news", it is important to begin with the facts. YouGov conducted its latest poll on Brexit on January 11 and 12. It found that the nation was indeed split and only marginally changed from the June referendum outcome. In this poll, 44 per cent of all voters said they would to Remain and 43 per cent said they would vote Leave. This is well within the margin of error (as was the June referendum itself), and there was little recorded movement from one side of the divide to the other.

By introducing the question of immigration the YouGov pollsters made the responses much more decisive, and quite at odds with the received wisdom on the issue. YouGov asked only Leave voters what is the maximum amount of money they would be willing to lose "in order to regain control of immigration". The responses ranged from nothing at all to accepting a loss of over £200 or month per month and all points in between. The clear majority opted for nothing at all. They were willing to make no financial sacrifice at all.

Remember, this is solely among Leave voters. It cannot be ruled out that some minority of Remain voters are willing to give up income to see immigration. But this would surely be a minority, possibly a tiny one. Therefore, the overall majority of voters, Leavers and Remainers combined are not will to let their living standards fall in order to lower immigration.

This stands in complete contrast to widespread assertions that the narrow Leave win in the referendum was "really" about curbing immigration. Theresa May herself has said that voters gave a very clear message they wanted tighter controls on immigration. But of course immigration was not on the ballot. We know that popular sentiment is not pro-immigration. How could it be when voters have been told for years that it is the cause of all their woes?

Still, the clear evidence from the latest YouGov poll (and others) is that voters are unwilling to accept any decline in their living standards to achieve lower immigration. This makes it clear that immigration is not the paramount issue. Living standards are, as they usually are.

This has clear implications for all political parties. YouGov’s poll shows us that Labour cannot win by promising to cut immigration at the expense of living standards, which would surely follow any decision to quit the single market. Indeed, 65 per cent of the 2015 Labour voters voted to Remain. Among the minority Labour Leavers, two-thirds would not be willing to see any fall income in order to reduce immigration. The net result is that just 1 in 10 Labour voters in 2015 are willing to cut see their incomes fall to curb immigration.

Labour’s winning strategy will be to focus on its economic programme for government. Our electoral strategy will show people how Jeremy Corbyn and John McDonnell's economic plan can make the overwhelming majority of people better off. And keep on showing them. The reactionary Tory agenda can only make people worse off.