Liz Kendall tells BI she believes Jeremy Corbyn will pledge to keep Britain in the single market and customs union.

"I know the leadership is very concerned with being a democratic party and I believe they will listen to the members on this," Kendall said.

Kendall, who ran to be Labour leader in 2015, said Jeremy Corbyn will "go further" towards a soft Brexit.

The Labour MP said she would also support a second EU referendum: "That's not something I'm against."

LONDON — Former Labour leadership candidate Liz Kendall has challenged Jeremy Corbyn to listen to party members and commit to keeping Britain in both the single market and customs union after Brexit.

The Labour leader has so far resisted calls to soften the party's policy on Brexit, despite polling suggesting that both Labour members and voters are increasingly pro-EU.

However the former shadow Cabinet member told BI that she believed Corbyn would soon shift his position and listen to party members calling for him to soften the party's position.

"I know the leadership is very concerned with being a democratic party and I believe they will listen to the members on this," Kendall told BI.

She said the party needed to create a clear dividing line on Brexit with the Conservatives.

"We have already rightly said that Britain should remain in the single market and customs union during the so-called transition," she said.

"I believe that we'll end up going further because we have to have a clear alternative to the Conservatives."

Labour's current policy is to remain in both during a transition period but has not yet set out in detail what it wants Britain's post-Brexit relationship with the European Union to be. 87% of Labour members want to stay in the single market and customs union, according to a poll published earlier this year.

You can't be anti-austerity without being for remaining in the single market and customs union.

The MP for Leicester West is among a chorus of Labour MPs including Chuka Umunna, Alison McGovern and Heidi Alexander who are urging the party leadership to embrace a softer Brexit policy in line with party members.

In an interview with BI in December, Umunna warned that leaving the single market and customs union would "torpedo" Labour's spending plans outlined in its most recent manifesto.

Kendall echoed her colleague, warning that "you can't be anti-austerity without being for remaining in the single market and customs union."

She said: "A jobs-first Brexit deal means remaining in the single market and customs union. It's what is vital for our public services because if we get an economic downturn we won't be able to invest in that.

"If you believe in a strong economy, bringing money again that we need to invest in the NHS, schools, social care and crumbling infrastructure, we need to stay in the single market and customs union."

A second referendum? "That's not something I'm against"

Kendall, who spoke to BI at a conference hosted by research group UK In A Changing Europe, suggested she would support a second referendum on Britain's membership, saying: "That's not something I'm against."

The prospect of a second vote has been talked up in recent weeks after former UKIP leader Nigel Farage said his "mind is changing" on the issue as a second vote could "kill off" the argument for good.

Corbyn is not currently in favour of a second referendum, but he has not ruled it out either. "We’re not asking for a second referendum," Corbyn told Andrew Marr over the weekend.

However, Kendall suggested that a nationwide vote on the terms of the final deal was now more likely than ever before.

"The possibility of it is now on the agenda like it wasn't a few months ago," she said.

"I think there are real issues with referendums. Like seeing Nigel Farage and cronies pile in with lies and information like £350 million for the NHS on the side of a bus.

"But the principles of there being a final say — whether that being in Parliament, where it must happen, or in the country — is more of a possibility than we've seen before."