Jeremy Corbyn has rightly said that Labour’s position on Brexit is to focus on a deal that prioritises jobs first. We are all united behind that goal. For us that means membership of the single market. A country can be a member of the single market without being a member of the EU and we must be clear – “access” to the European single market is both different and inferior to “membership” of the single market. Why? Because if we leave the single market, whatever the level of access is negotiated, working people across Britain will be worse off and revenue to the exchequer will plummet – revenue the next Labour government will need to bring an end to years of damaging Tory austerity.

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The single market is not a simple free trade zone. It is, uniquely, a framework of rules that protects people from the worst excesses of globalisation and unfettered capitalism, in addition to easing trade across the continent. If we have mere access to the single market, we are talking about leaving this framework of rules and achieving mere reductions in tariffs for trade with the European Union.

If Britain stays in the single market, we will continue to benefit from EU laws and court judgments that outlaw discrimination in the workplace; deliver vital rights to workers on holiday pay, maternity and paternity leave, the right to join a union, and much more; protect our natural environment from pollution; and keep workers safe through stringent health and safety requirements. Large multinational companies work across borders to maximise their profits to often reduce these protections; the next Labour government, as a member of the single market, can work with other European countries to resist this and advance social justice. If we leave the single market, and ask for mere “access”, we will be compromised in achieving these goals.

This is why so many people in the Labour movement are supporting British membership of the single market after Brexit. Frances O’Grady, the general secretary of the Trades Union Congress, has said that “if we leave the single market, working people will end up paying the price. It’d be bad for jobs, for work rights and for our living standards.” The USDAW trade union has warned that leaving the single market “will put at risk hundreds of thousands of jobs”.

And who is leading the charge to junk our membership of the single market? A motley crew of hard-right, pro-Brexit Tories. Michael Gove. Boris Johnson. John Redwood. Iain Duncan Smith. Priti Patel. Theresa May wants us out because her government is totally dominated by its obsession with leaving the single market. They want us to leave precisely because they want to roll back the social protections delivered by single market membership. Redwood authored a plan to cut regulation in Britain by 25%. Patel went one further, calling on the “burden” of EU regulations – those rules that protect working people – to be “halved”. We should not be providing political cover to hard-right Tories who stand diametrically opposed to Labour values.

The argument for leaving the single market is often focused around the need to end the free movement of people. However, we argue, and many experts agree, that changes to our immigration system can be made while keeping us inside it. Within the European treaties, free movement is not unconditional – at the moment we can require EU citizens to leave if they have no job or a prospect of a job three months after their arrival. Restrictions on free movement are explicitly allowed for reasons of “public policy, public security or public health”. Liechtenstein, which is outside the EU but in the single market, perfectly legally imposes quotas on EU migrants. French president Emmanuel Macron’s chief adviser has floated the idea of a “continental partnership” between Britain and the EU that would allow us to restrict free movement.

Another reason often cited for not remaining a member of the single market is that the state aid rules that apply in it stop governments from pursuing active industrial strategies to support their industries. But these have not stopped the likes of Germany having a national investment bank or France and the Netherlands supporting their industries through government procurement spend.

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Ultimately, leaving the single market will make it much harder for a Labour government to end these years of Tory austerity. The economic damage it would cause would reduce the tax take, meaning less money could be spent on public services. The respected Institute for Fiscal Studies has forecast that leaving the single market for a free trade agreement could cause a £31bn hit to the public finances, extending austerity even further.

To win next time, Labour must provide a strong opposition to the Tories, stand up for the values of our voters, and continue to fight for the interests of all – not least young people who have the most to lose from an extreme Tory Brexit and who voted for the first time in 2017 for Labour, thinking we would stop the Tories in their tracks. This has to mean fighting unambiguously for membership of the single market. At the very least we should strongly oppose May’s decision to take membership off the table in these negotiations. An ambitious and confident alternative government – with Corbyn at the helm – should not throw in the towel as May has done, but could seek membership with reforms on immigration and the other matters we seek.

• by Chuka Umunna MP, Phil Wilson MP, Madeleine Moon MP, Maria Eagle MP, Liz Kendall MP, Stella Creasy MP, Wes Streeting MP, Mike Gapes MP, Kate Green MP, Lord Michael Cashman, Anne Coffey MP, Ian Murray MP, Rushanara Ali MP, Karen Buck MP, Stephen Doughty MP, Stephen Timms MP, Lord Spencer Livermore, Catherine McKinnell MP, Lord Peter Hain, Tulip Siddiq MP, Peter Kyle MP, Ruth Cadbury MP, Bridget Phillipson MP, Pat McFadden MP, Ann Clwyd MP, Thangam Debbonaire MP, Chris Bryant MP, Andy Slaughter MP, Daniel Zeichner MP, Alison McGovern MP, Darren Jones MP, Kerry McCarthy MP, Ben Bradshaw MP, Clare Moody MEP, Seb Dance MEP, Luciana Berger MP, Lord George Foulkes, Catherine Stihler MEP, David Martin MEP, Jude Kirton-Darling MEP, Mary Honeyball MEP, Paul Brannen MEP, Richard Corbett MEP, Julie Ward MEP, Derek Vaughan MEP, Lucy Anderson MEP, David Lammy MP, Lord John Monks, Meg Hillier MP, Adrian Bailey MP and Lady Meta Ramsay