IT’S the EU that guarantees workers their rights to paid holidays, parental leave, equal treatment for part-timers, and much, much more.

Unions campaigned hard to win these rights from the EU. Some of them resulted from direct negotiations between unions and employers at EU level. We should be proud of achievements born out of solidarity with European unions, through the ETUC.

The EU’s origins may have been a common market, but as Jacques Delors’s famous speech to the Trades Union Congress in 1988 signalled, it became something much more.

His speech caused consternation among free market, deregulation-obsessed conservatives. Delors said that that the free market must have rules, that Europe must deliver real benefits for workers, and that trade unions should have an equal place at the table.

A succession of EU directives has driven progress on workers’ rights and equality in Britain — often further and faster than any British government of any stripe was prepared to go.

So now the question is, if we left the EU would you trust the current Conservative government to keep them? If the Brexit camp gets its way, the British government would get to pick and choose which rights to water down or scrap altogether.

Without an EU legal safety net it wouldn’t be long before bad employers started cutting back on paid holidays, pushing workers to work longer hours with fewer breaks, and stopping pregnant workers getting time off for medical appointments.

Unions would not have the chance to extend workers’ rights through the European Court of Justice (ECJ), as we have done on equal pay and working time. And our collective agreements that build on these legal minimums would be under threat.

That’s why the TUC is warning workers about the risks of Brexit. Workers have a lot to lose.

That doesn’t mean we’re starry-eyed about the EU. We are critical of the EU’s privatisation and austerity policies.

Let’s not forget that it’s Britain’s governments that were the chief champions in Brussels arguing for them. And, as internationalists, trade unionists know that our chances of fending off the neoliberals at home are even worse if we’re on our own.

Lots of our rights at work are guaranteed by the EU and it would be a mistake to take them for granted. As the TUC’s annual Women’s Conference begins today, let’s look at what EU membership means for female workers.

Gender equality rights are underpinned by EU law, meaning they can never be dismantled so long as Britain is in the EU.

The right to paid time off for antenatal appointments came directly from the EU.

And while the maternity leave entitlement in Britain already exceeded the EU minimum of 14 weeks, case law from the ECJ has helped tackle the disadvantage and discrimination many women workers face when they become mums.

The ECJ made clear that treating a woman unfavourably because of pregnancy or maternity leave is direct sex discrimination. This ended years of women being defeated in discrimination claims because the employer argued that they would have treated a man who had to take a substantial period out of the workplace in a similar way.

And it meant that British law was changed to make pregnancy discrimination a separate category.

ECJ case law has also extended protection from dismissal on grounds of pregnancy or maternity leave to fixed-term workers. And, since 2008, women on additional maternity leave have had access to the same contractual rights as women on ordinary maternity leave as a result of ECJ case law. This means, for example, that employers are obliged to make contributions into occupational pension schemes for longer than the first 26 weeks of leave.

The current government has already shown its appetite to attack workers’ rights. It’s cut TUPE — protections for workers when their organisation changes hands — for outsourced workers, hiked up tribunal fees and extended the period before which workers can qualify for unfair dismissal claims.

Without the back-up of EU laws, unscrupulous employers will have free rein to cut many of their workers’ hard-won benefits and protections.

And the same goes for the good jobs that depend on EU investment. Being in the EU is one major reason why we export so much to the rest of Europe, and the bigger our export market is, the more jobs there are in those industries. Jobs in exporting industries pay more than the average, and are more skilled.

Just ask workers in the car industry whether they think companies are bluffing when they say they would relocate, or focus future investment decisions elsewhere. There is no simple model for Britain’s trade with the EU from outside of it. The costs would rise and there would be consequences in terms of jobs, pay and conditions.

Some friends in the movement take a different view on the EU. I respect their views. And both sides of the debate have been too dominated by big business. I worry too that the migration debate is being hijacked by those who see free movement as just another source of cheap labour in one corner, and those who want to blame migrant workers for all our ills in the other.

As trade unionists, whichever way we intend to vote, we must unite in pointing out that migrant workers aren’t to blame for undercutting wages — the bosses who exploit them are.

Of course, no-one thinks the EU is perfect. In recent years, the pace of social reform has slowed. The TUC has been a stalwart opponent of TTIP, and of the treatment meted out by the European Central Bank to Greece.

We want the EU to do more to raise the quality of work and to increase the supply of jobs in every member state and to spread industrial democracy. And we need the EU’s heads of state to recognise the failings of EU-wide austerity, and focus instead on the investment needed for fair and greener growth.

But staying in offers the chance to rebuild a vision of Europe for workers, regardless of the passport they hold. As the EU Left begins to debate a new social pillar of rights and protections, we want to be part of that campaign to make it happen. A vision of Europe fit for the 21st century and a practical plan to deliver strong rights, decent jobs and livelihoods, with strong unions at its heart, is one worth fighting for.

• Frances O’Grady is general secretary of the TUC.