Britain's Defence Secretary Liam Fox leaves his residence in central London, October 13, 2011. [Photo/Agencies]

"Existential crisis"

Labor's deputy leader Tom Watson said the party, which cruised to three back-to-back election victories under former leader Tony Blair between 1997 and 2010, risked an "existential crisis" as Corbyn refused to bow to pressure to resign.

Corbyn, a veteran hard-left Labor lawmaker, is unpopular with many Labor MPs, who passed a motion of no confidence in him this week.

But he commands strong support among party activists who helped him to take over in 2015, raising the prospect of a continued stalemate within Labor over his leadership.

Cameron said on Wednesday it was bad for the country to have a weak opposition party. "For heaven's sake, man, go," he told Corbyn in parliament.

Corbyn won control of Labor with the help of trade unions after the party lost a national election last year.

In a joint statement on Wednesday, the leaders of 10 big unions said the crisis within Labor at Westminster was "deeply regrettable and unnecessary" but stopped short of saying Corbyn's grip on the party should not be disputed.

"His position cannot and should not be challenged except through the proper democratic procedures provided for in the Party's constitution," the statement said. "We urge all Labor MPs to abide by those procedures, and to respect the authority of the Party's Leader."