The main finding from our poll, carried out in the middle of last month, is that immigration is uniting the right but dividing the left. Based on the answers given on a range of issues, we were able to separate people into eight political tribes. The two largest we identified were on the right of British politics, and make up half of the electorate. While they disagree about some economic issues, they are broadly united in favour of leaving the EU and reducing immigration sharply.

One (we call it Common Sense, 26% of those polled) is made up overwhelmingly of Conservative voters, mainly older people from the south of England who are advanced in their careers or retired. The other (Our Britain, 24%) mostly comprises older working-class people from the north of England and the Midlands, and is split between Tory and Ukip voters. Both would prioritise reducing immigration over remaining in the EU single market. Interestingly in the light of last week’s announcement, both would also favour more grammar schools. They represent a solid core of rightwing votes.

Closer to the centre but still on the right of it sit two smaller pro-business tribes (Free Liberals, 7%) and New Britain (6%). These two groups agree with the Common Sense group about the need for low taxes and restricting benefits but are much more pro-immigration, voted Remain in the referendum and want Brexit to mean staying in the single market. But both are overwhelmingly pro-Conservative in their political outlook and there isn’t really any other party that is a natural fit so they are unlikely to drift away. Theresa May has a large pool to fish in and plenty of options.

By comparison, and looking at the tribes further on the left, the situation faced by whoever wins the Labour leadership will be far harder because the centre and the left are split into more tribes with bigger divisions. The ones Labour will target are split over immigration, business, and whether Britain should be an open multicultural society or a closed, ethnically homogenous one. They are also divided geographically between those in Scotland, the urban north (more anti-immigration) and the metropolitan, more multicultural south.

The tribes on the left include one we call Democratic Socialists (8%) who are very open to immigration and the single market but also want higher taxes on the wealthy and businesses. They are mostly ABC1s, living in urban areas in Scotland and Wales. Then there is the Community tribe (5%) – mainly working-class voters in northern England and the Midlands – who agree on the need for income redistribution through the tax system but strongly disagree with the Democratic Socialists about immigration, wanting strict curbs.

Another tribe, the Progressives (11%), are professionals from across the country, who share the Democratic Socialists’ openness to immigration and the single market but are much more pro-business.

In the 1990s, it was possible to put together a coalition of these tribes on the left and centre-left and win over enough in the Swing Voter tribe (7%) to form an election-winning majority, as Tony Blair did. But we now live in a world in which views on immigration have polarised and many in the north feel left behind and threatened by multiculturalism and globalisation, while more in the south embrace both.

The left is divided not just from the right, but among its composite parts. From our findings – 6% of the population did not fall easily into a “tribe” – it will be a lot easier to form a winning majority of centre-right and rightwing tribes than centre-left and leftwing ones. So, despite facing the most daunting inbox of any prime minister for decades, our poll is good news for Theresa May but far less promising for whoever takes Labour into the next general election.

Adam Drummond is research manager and partner at Opinium