Nick Timothy has a wizard wheeze to keep the Conservative Party alive: that it must reorient itself as a socially conservative and economically redistributive party committed to Brexit. He’s the latest in a series of political figures from across the political divide to suggest that their party should recreate itself as a “pure” party of the Brexit divide, solely committed to either Remain or Leave.

That the idea is repeatedly mentioned means that it is worth looking at in greater detail. Could it work?

The first problem, from a policy perspective, is that it is hard to see what the present-day Conservative Party could do to “embrace Brexit” that it is not already doing. Some 235 Conservative MPs have now backed the withdrawal agreement, a negotiated exit from the European Union that takes the United Kingdom out of the European Court of Justice, the Common Agricultural Policy, the Common Fisheries Policy and the single market. Another 66 Conservative MPs have voted against it on the grounds that this Brexit does not represent a sufficient breach from the European Union. That is, by any stretch of the imagination, a party that has not only embraced Brexit but has gone further than public opinion – no pollster has found that no deal is more popular than a negotiated exit from the European Union.

If the requirement for “embracing Brexit” is that the Conservative Party finds a Leave position that various other pro-Leave forces won’t denounce as a betrayal, then there’s a problem: this position does not exist. There is no Brexit position that Nigel Farage won’t denounce because it is in his wider political interests to do so.

Moving towards “Leave voters” on economic grounds presents a similar problem. As Bristol University’s Paula Surridge has shown, there is no left-right difference between Remain voters and Leave voters. Conservative supporters of Brexit are just as right-wing on issues of economic policy as Conservative Remainers are. Labour opponents of Brexit are just as left-wing on economic issues as Labour voters who backed a Leave vote are.

So moving “towards Leave voters on economics” actually just means moving towards all Labour voters on economics, and hoping that the movement gains current Labour voters at a faster rate than it loses Conservative ones, whether to direct defection to parties to the Conservatives’ right flank or to non-voting.

What actually divides Remain voters and Leave voters is not economics but cultural concerns: Leave voters are, in the main, socially authoritarian, while Remain voters are, for the most part, socially liberal.

The pattern within the two parties’ coalitions are subtly different, however. Labour supporters form two distinct blocs on social issues: a socially liberal cluster of young people, the big city working classes, and graduates of all ages; and a socially authoritarian cluster of older voters, small town working class voters and non-graduates, with very few voters falling in between. The Conservative electoral coalition is more like a Dulux colour chart: becoming more socially liberal among Remainers and more socially authoritarian among Leavers, but with much less polarisation between the two.

So the problem here is that to be as socially authoritarian as the “Labour Leaver” cluster, you’d have to be a lot more socially authoritarian even than a number of Conservative voters. Again, you’d be making a big bet that you wouldn’t lose Tory voters at an equal or faster rate to gaining Labour voters. The 2017 election showed that, while the Tories could gain Labour votes this way, they also lost 2015 Conservative votes with the same approach. To make matters worse, the Conservatives lost voters in seats where Labour was relatively close behind, while they gained votes in seats that they still couldn’t win. The same pattern could well recur.

It’s also not clear what cultural issues the Conservatives can actually set up as dividing lines with Labour. On the death penalty, large numbers of Tory MPs are opposed to bringing it back, and to commit to doing so you would need to replace not just the minority of Conservatives who want to stay in the EU, but MPs across the party. The same is true of abortion, reproductive rights, and non-traditional family types. On gender issues, it is a Conservative select committee chair, Maria Miller, and a Conservative government that is pursuing changes to the Gender Recognition Act. On immigration, both parties are committed to ending the free movement of people after we leave the EU.

When people – both inside and outside Labour – talk about the left’s focus on identity politics it seems as if they are talking about a Labour Party that has ceased to exist, if it ever did. Jeremy Corbyn is not someone who gets het up about “new” left issues and has shown a consistent willingness to occupy positions on identity and security – for instance by linking support for ending austerity to opposition to police cuts, or his commitment for bank holidays to mark our national saints’ days or the success of the England football team – that make it hard to outflank him.

Focussing on economics and culture actually cancels out the appeal made by reaching towards Labour voters on cultural issues. If the question in the mind of voters is “Who is tough on immigration?” then it might be enough to peel away a decisive chunk of Labour Leavers. But if the question is “Who is tough on immigration, and is economically redistributive?” it can actually reinforce the pre-existing two party division, of economically redistributive voters backing Labour and economically conservative voters backing the Conservatives.

Added to that risk, while it is easy to type the phrase “move towards Labour voters on economics” it is a lot more difficult to do that in practice. The Conservative Party has no parliamentary majority of any kind, and many of its sitting MPs are committed economic liberals. The Labour Party isn’t going to vote to facilitate a move towards its own territory by the government of the day because that would be tactically inept.

So what “move towards Leave voters on economics and culture” means in practice is “bring forward legislation that your own MPs won’t back for ideological reasons and the opposition will oppose for tactical purposes, have a bruising civil war on cultural issues in your own party, flop about failing to legislate for three years, then go to the country and ask to be re-elected”. That’s not a strategy to revitalise the Conservative Party, but to finish it.