Jeremy Corbyn today faces calls from across the Labour movement to commit to full and permanent membership of the EU single market and customs union – so the party can offer a clear alternative to the Tories over Brexit.

As Labour’s annual conference opens in Brighton, more than 30 MPs, together with MEPs, Labour peers, trade union leaders and mayors, publish an open letter demanding that Labour shows “the courage of its convictions” and toughens its pro-EU message.

Brexit looks certain to provoke the most heated debate in Brighton as delegates gather in buoyant mood following the party’s performance in June’s snap general election.

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Writing for the Observer, Corbyn says his party is now “a government in waiting”. He urges all Labour members “to use our new strength inside and outside parliament to challenge the Conservatives at every step – and prepare to form a new government to change Britain whenever the next election is called”.

He adds: “Our mission must be to work with the people of Britain to transfer wealth, power and opportunity to the many from the few. For the first time in a long time we can provide a politics of hope and a politics for the people.”

But divisions over Brexit were already surfacing on Saturday night as pro-EU delegates demanded that they be given the chance to vote on a change to official Brexit policy on the conference floor.

In their open letter the MPs and senior figures in the Labour movement, including former shadow cabinet members Heidi Alexander and Chuka Umunna, as well as one of Corbyn’s closest allies in his early days as leader, Clive Lewis, say it is “unsustainable to say we are an anti-austerity party” while being in favour of leaving the single market and customs union.

The letter, also signed by the TSSA union’s general secretary, Manuel Cortes, former Northern Ireland secretary Peter Hain and Liverpool mayor Joe Anderson, says Labour should stand up for the principle of free movement of workers and reject totally the Tories’ “destructive Brexit”.

They say: “So at our conference this week, Labour should commit to staying in the single market and customs union – ruling out no options for how to achieve this – and to working with sister parties and others across Europe to improve workers’ rights, boost trade union membership and put an end to the exploitation of workers, not freedom of movement.

“This would send a powerful message of solidarity to the rest of Europe, and to the millions of EU and UK nationals living in limbo here and across the continent.”

Only five weeks ago, Labour’s Brexit spokesman, Keir Starmer, rewrote Labour’s policy, committing the party to remaining in the single market and customs union during a transitional period of between two and four years, and keeping open the possibility of long-term membership if a new deal could be negotiated to reform free-movement rules.

But signatories to the letter, organised by Open Britain and the Labour Campaign for the Single Market, while welcoming Starmer’s move, say the party remains insufficiently distinct from the Tories on Brexit.

Pressure for Labour to go further has mounted since Theresa May used a speech in Florence on Friday to propose a two-year transition after 2019 during which the UK would in effect stay inside the single market and customs union. After the prime minister’s speech, Starmer accepted that the Tories had adopted Labour’s plans.

Calls for the party to back single market and customs union membership could potentially put Corbyn, who has in the past been lukewarm in his support for the EU, at loggerheads with much of the party’s mass membership, which backed Remain in the referendum last June. More than 40 motions on Brexit have been submitted for debate at the conference. A decision on the wording of a motion to be debated on Monday will be discussed behind closed doors by party officials and MPs on Sunday night.

Corbyn is under pressure from some of his own supporters to back the EU’s free movement of labour rules, which the party vowed to tear up in its last election manifesto. Among those pushing for a vote on the issue at Labour’s conference is Michael Chessum, formerly a senior figure in the Corbyn-supporting Momentum group.

On Saturday the Tories’ fragile truce over Brexit was already fracturing as allies of Boris Johnson declared that the foreign secretary had dramatically altered the prime minister’s keynote speech on Europe and forced the cabinet to accept a shorter transition period.

They said that before his 4,000-word essay setting out the need for a hard Brexit, the government had been heading for a future in which it would have been out of the EU “in name only”. Friends of the foreign secretary also took aim at Philip Hammond, accusing the chancellor of pushing a plan for a transition period lasting four or five years, rather than the two-year period announced by the prime minister.

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Allies of the chancellor were adamant that Hammond had been pushing no such plan, pointing out that he had been publicly advocating a transition period of two or three years. Downing Street sources also denied May’s speech had been rewritten as a result of Johnson’s intervention.

Meanwhile, there are increasing concerns in the Tory ranks that not enough work is being done to prepare for the possibility of crashing out of Europe with no deal.

Sir Oliver Letwin, the former cabinet minister who was in charge of the Whitehall unit charged with preparing to leave the European Union under David Cameron, told the Observer: “My sense talking around is that the work is beginning inside HMG now, but I don’t believe it has yet reached anything like the level of intensity that it needs to reach.

“That is OK – there is still time , but it will have to be done in the next few months. It requires clear thinking and administrative competence.”

Despite the concessions made by May, several government insiders said they believed that the EU would not agree to sanction talks over a future trade deal next month, Instead, insiders now hope the talks will being before Christmas.