Research by YouGov for The Times newspaper said Mr Corbyn is the first preference for 43 per cent of party supporters compared to Ms Cooper on 20 per cent.
But the shadow home secretary said the poll didn’t match her own private research and warned that for the party to shift to the left in the wake of their general election defeat could see it return to the ‘dismal days of the 1980s.’
A spokesman for Ms Cooper said: “This doesn’t reflect our internal data and significantly understates the huge number of members and supporters giving Yvette their first preference. However, what it does show is that Yvette is now the only candidate who can win the leadership election and then reach out to the wider electorate to win the general election in 2020.
“We won’t do that by shifting a narrow party further to the left or by returning to the dismal days of the 1980s, with internal party warfare and almost two decades of Opposition. Party members know that to change the country, we need to deliver a Labour government.
“Yvette is the only candidate who can both win support across the party but take the fight to the Tories as a credible Labour Prime Minister.”