Labour supporters of close ties with Europe have issued a challenge to Jeremy Corbyn to “get off the fence” and commit to keeping Britain in the single market and customs union after Brexit.

And they challenged what they claimed were “myths” being spread by the so-called “Lexit” lobby, which campaigns for Britain to leave the EU on left-wing grounds.

Mr Corbyn is coming under increasing pressure to clarify his position that he wants a “jobs-first Brexit” which allows Britain to retain the benefits of the single market and customs union.

The Labour leader backed Remain in the 2016 referendum, but has previously indicated that he believed EU state aid rules would tie the hands of a left-wing government which wanted to offer support to home-grown industries.

The co-chairman of the Labour Campaign for the Single Market, Heidi Alexander MP, said:  “We have to be honest.

“There is real frustration out there amongst Labour members and supporters about the party’s position on Brexit.

“The sooner the leadership recognise this, the better it will be for the country.

“At no point in my lifetime has the opposition’s policy on an issue been more important.

“The fact that we continue to hedge our bets, when the argument is there to be won, is not doing anyone any favours.

“We need to remain in the customs union, meaning no tariffs on goods traded between the UK and the EU, and we need to stay in the single market, so our service industries can continue to trade freely and easily.

“If we don’t get our act together we will see jobs go, the tax-take fall and public services cut further – we can’t let that happen.”

The group’s other co-chairman, Alison McGovern, said: “It is time for Labour to get off the fence.

“To end any perception that our party is on the same side as the purveyors of falsehoods like Boris Johnson and Michael Gove we need there to be a real difference between our party’s policy and that of Theresa May.

“Words about a ‘jobs-first Brexit’ are in danger of looking like nothing more than clever rhetoric unless Labour actually backs the policies that will put jobs first by keeping us in the single market and customs union.”

The LCSM joined with pro-European group Open Britain to produce a pamphlet entitled Busting the Lexit Myths, which rejects as “mistruths” the claims that:

::  EU state aid rules would prevent Labour having an active industrial strategy;

:: Austerity is a consequence of EU membership;

:: The EU would block renationalisation of the railways;

:: Labour could strike “more progressive” trade deals if Britain leaves the customs union.

Authors include former shadow Foreign Office minister Catherine West, the leader of the European Parliamentary Labour Party Richard Corbett MEP, and Lord (John) Monks, the former general secretary of the TUC.