Just over a third of Labour backers said Corbyn should stand down immediately, and 14 per cent said he should quit ahead of the next election.
And just 44 per cent of Labour members said the current Labour leader should take the party into an election in research by Election Data and YouGov.
It comes just days after Labour suffered a historic defeat in the Copeland by-election, the first of its kind since the 1980s.
And 41 per cent of those polled suggested that Corbyn was directly to blame.
But in spite of this, the Labour leader still retains significant support, with 54 per cent of party members saying they approve of his leadership. 37 per cent disapproved.
And critically, of those who voted for Corbyn in the party's most recent leadership election, a huge 81 per cent said they would do so again.