About two in five voters would be highly likely to vote for a new party in the political centre ground at a future election, a new poll for the Observer has revealed.

Just over a third (35%) also say they felt unrepresented by the existing main parties on offer, according to the latest Opinium poll.

It suggests there is appetite for a new party, with both Labour and the Tories suffering from long-running internal strife. While there is regular talk of new parties and splits, many possible supporters are put off by the difficulties of making a new project work under Britain’s first-past-the-post electoral system.

The poll also reveals that almost half of voters do not see strong leadership from the two main parties, with 47% believing Theresa May is not a strong leader and 49% regarding Jeremy Corbyn as a weak leader.

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The findings come with the Lib Dems attempting to pitch themselves as the right vehicle for moderates put off by the civil wars inside the Tories and Labour. The party’s annual conference starts this weekend, but it has failed to capitalise on the divisions inside its rivals.

Facebook Twitter Pinterest Lib Dems leader Vince Cable in London, England. Photograph: Dan Kitwood/Getty Images

Speaking before his party conference in Brighton, Vince Cable said he wanted to “make an open pitch to the people of this country who are fed up with the extremes of the current Conservative and Labour parties”.

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“Whether you see yourself as a liberal, social democrat, progressive, or centrist, there is a home for you here, particularly as we fight Brexit together,” he said.

Despite the difficulties that any new party would face, talk of such a move has not gone away. Some Labour MPs have privately said they will look again at the idea once Brexit has happened in the spring.

Asked to imagine that a new centre-ground party formed tomorrow, two in five voters (42%) said that they would be likely to vote for it in a future general election.

The poll found that the Conservative party is seen as equally as divided as Labour. Almost three in five (57%) think the Tories are divided, up from 47% in December 2017. The same proportion (57%) think that Labour is divided, up from 40% in December 2017.

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Overall, the Tories retained their one-point lead in the poll recorded last month. May’s lead over Corbyn on who would make the best prime minister has increased from last month, rising from six points to nine points.

However, May has suffered a fall in the number of those who think she is decisive, down from 41% in April to 29% this month. It means she only has a one-point lead over Corbyn in terms of who voters regard as a decisive leader.

Opinium polled 2,011 adults online between 11 and 13 September.