Strongly working-class parliamentary seats are no longer the Labour party’s heartlands as its core support has shifted to big cities, according to new analysis of the changing face of the party’s base.

Support for Jeremy Corbyn’s party has been growing for years in large urban areas but falling in the most working-class seats, according to a study of constituencies in England and Wales by the Fabian Society thinktank, which is affiliated to the Labour party.

Its research also revealed a “growing hostility” between Labour’s old and new core voters, creating a tension at the heart of the party, which has been riven by internal strife over its direction since 2015.

The report warns that the tensions are so acute and unresolved that they risk costing the party the next election.

The growing parts of Labour’s core support were also likely to be the least loyal, the report found, suggesting the party faces a tough choice over how it appeals to the working-class heartlands that have stuck by it.

The tensions in its coalition of supporters have been inflamed by Brexit. Senior figures are concerned that enthusiastic support for a soft Brexit or a second referendum, demanded by many of its supporters, could alienate some working-class communities that have continued to back it.

It is a conundrum, once referred to by the Manchester mayor Andy Burnham as the rift between “Hampstead and Hull”, which continues to torment the party.

The Fabians report, For the Many?, attempted to build a comprehensive picture of Labour’s base, through analysis of voting data and interviews with supporters.

Support in the 63 most working-class seats has dropped noticeably. These have seen a swing to the Conservatives of 3.6 percentage points since 2005. Labour holds 57 of the 63 seats, down from 62 in 1997.

Meanwhile, in a group of 40 seats in hub cities including Birmingham, Bristol, Cardiff, Leeds, Liverpool, Manchester, Newcastle Upon Tyne and Sheffield, Labour’s position has been strengthening – especially in seats with high concentrations of young people and in places with growing numbers of black and minority-ethnic voters. In these areas, there has been a swing to Labour of 5.6 percentage points since 2005.

In 2017, in England and Wales, every seat in these cities returned a Labour MP, the first time this has ever happened. It finds that big-city seats are Labour’s new heartlands.

In the 24 seats in “middle” London – those in the capital excluding the extremes of affluence and poverty in the west and east of the city respectively – there has been a swing to Labour of 9.7 percentage points since 2005.

The report also suggests that Labour’s surge in support from Remain backers has been overestimated. It states that the most remain-leaning seats started to move to Labour well before the referendum, suggesting demographic factors are more crucial than the EU vote.

In-depth interviews with Labour voters revealed a bubbling tension between different types of supporters.

For newer metropolitan supporters, the test of their support was that the party is “relentlessly liberal and open minded”. For those in its old heartlands, the test is whether the party is “willing to conserve community and industry”.

Report co-author and Fabian Society deputy general secretary Olivia Bailey said the research revealed “how fragile Labour’s coalition has become over a decade and more”.

“To win the next election, Labour must build on its progress in affluent and city seats as well as take action to arrest its decline in working-class areas,” she said.

“This means building an offer that speaks to the shared values of Labour supporters, rather than playing to the differences.”

Lewis Baston, the political analyst and co-author, said: “Labour racked up huge majorities in many urban constituencies in the 2017 election. But in working-class seats Labour majorities were wearing thin. Preserving and extending the impressively broad coalition of people who voted Labour in 2017 requires the party to keep finding policies and themes that unite its old and new supporters.”