A wave of lawmakers from the opposition Labour Party resigned in protest from leader Jeremy Corbyn's team on Monday, including his most senior business policy chief who said Corbyn was partly to blame for last week's vote to leave the EU.

Corbyn has resisted pressure to quit over what critics say was his lacklustre effort to keep Britain inside the European Union, saying on Sunday that he would stand again in any leadership election triggered by the party revolt.

"Too many of our supporters were taken in by right-wing arguments and I believe this happened, in part, because under your leadership the case to remain in the EU was made with half-hearted ambivalence rather than full throated clarity," wrote Angela Eagle, Corbyn's top business spokeswoman, in a resignation letter she later posted on Twitter.

Eagle was one of at least 16 members of his shadow ministerial team to have resigned in the last two days. All of those resigning will remain elected members of parliament.

Corbyn was elected party leader last year on a surprise wave of grassroots enthusiasm for his left-wing agenda and promise of a new approach to politics. But his relationship with elected lawmakers has always been fragile, with many questioning whether the party could win a national election on such a ticket.

Amid the flurry of resignations, Corbyn announced a number of appointments to replace those who quit on Sunday, promoting several members of his inner core of left-wing supporters to senior defence and foreign policy roles.

Sky News reported that Labour's deputy leader Tom Watson met Corbyn earlier on Monday to warn that he had lost the support of the party, and would face a brutal contest to replace him.