For all the fanfare and last-minute theatrics, the deal that David Cameron has made on Britain’s relationship with the EU is a sideshow. The changes he has negotiated are largely irrelevant to the problems most people in Britain face – and to the decision we now have to make.

Labour will campaign for Britain to stay in Europe in the referendum that the prime minister has called for June, regardless of Cameron’s overblown tinkering. That’s not because we don’t think the EU needs reform – far from it.

It’s because being part of Europe has brought Britain investment, jobs and protection for workers, consumers and the environment. We are convinced that the EU is a vital framework for European trade and international cooperation in the 21st century, and that a vote to remain in Europe is in the best interests of our people.

It’s easy to lose sight of those fundamental issues in the choreographed drama of the prime minister’s months of shuttle diplomacy, which were followed by Friday’s breakthrough-to-order. Cameron’s EU negotiations have essentially been about trying to appease his opponents in the Conservative party, rather than delivering the reforms that would make the EU work better for working people.

That’s why the Brussels deal is incidental to the real issues facing people in the referendum in June. The prime minister has been negotiating for the wrong goals in the wrong way for the wrong reasons.

He should have been talking to other European leaders about action to save our steel industry; about how to stop the spread of low pay and insecure jobs, and end the undercutting of wage rates and industry-wide agreements through the exploitation of migrant workers. He should have been focused on the scandal of the refugee camps in Calais and Dunkirk and how to deal with Europe’s migration crisis in an equitable way.

He could have been using Britain’s leverage to stop the threat to our services and rights in the secretive Transatlantic Trade and Investment Partnership (TTIP) negotiations; to build human rights and environmental protection into future trade treaties; and halt the pressure from Brussels to deregulate and privatise public services. He could have been arguing for an end to self-defeating austerity and for the strengthening of workers’ rights across Europe.

But of course he did none of these things. Instead his main concern in the talks over the rights of non-eurozone states has been to protect his friends in the City of London from financial regulation, including of bankers’ bonuses. Cameron’s Tories want a free-market corporate Europe. We want a social Europe of decent jobs and equality for all.

The evidence suggests that Cameron’s much-heralded “emergency brake” on in-work migrants’ benefits will do nothing to cut inward migration to Britain. Nor will it put a penny in the pockets of British workers. But there are dangers it could drive down pay rates still further as migrant workers take second jobs to make up for lower incomes – and that it could be extended to young workers in Britain on the grounds that they haven’t contributed enough to qualify.

David Cameron’s negotiations have been a missed opportunity to make the case for the real reforms the EU needs: democratic accountability, stronger workers’ rights, an end to austerity and a halt to the enforced privatisation of public services.

But it’s not Cameron’s deal that will be on the ballot paper in the referendum on Britain’s EU membership. In fact, it may not have even been finalised by June. People will be voting on far more important issues: jobs, investment, employment rights, environmental protection, peace, security and international cooperation.

Labour and the unions played a key role in making sure that employment rights – like guaranteed paid holiday, paid maternity and paternity leave, and agency workers’ protection – were kept out of Cameron’s negotiations. But there is a serious risk that the Tories would use a vote to leave as the chance for a bonfire of rights in its aftermath.

So Labour will be running a positive campaign for the real change we need: to unite opposition to austerity and build a Europe of sustainable growth, jobs and social justice. That can only be achieved by working with allies who share our aims across the continent.

We are already cementing those relationships with progressive leaders across Europe, as at the Party of European Socialists meeting I attended in Brussels on Thursday. It’s a long way from Cameron’s ideal of a continental corporate free-for-all. But it’s the Europe we will be campaigning and working for, in the referendum and beyond.