Britain’s immigration debate reverberates with arbitrary targets and dog-whistle politics. In the course of the Brexit negotiations, the focus has primarily been on exactly who gets to come here. The implication is that free movement is a problem rather than a process, and a one-way street flowing only into the UK. With negotiations proceeding, it’s important to ask before it is too late whether giving up our own freedoms without a fight is in Britain’s best interests.

Freedom of movement means that you can work for a company which has an office in Berlin or Rome, and it can send you there without any hesitation. It means if you fall in love with your French exchange partner, you can move to Paris or they to Barnsley. It means if you wanted to be one of the 4 million students who spend a year in another European country through the Erasmus scheme, you can. In the future the need for these freedoms will probably become more apparent, not less. Giving them up for perceived short-term political gain, and possibly doing long-term damage to the prospects of those who will rely on them, cannot be called progressive.

Many communities have changed as a result of immigration and asylum – but the benefits are overlooked, to all our detriment

The ability of EU citizens to come to the UK has also helped improve all our lives in ways which are now at risk. With a 96% drop in EU nurses registering to work in the NHS since the referendum, and an 86,000 vacancy rate in the health service and rising, we can’t train enough UK citizens to keep up with the demand for medics we now have. Far from preventing the undercutting of wages, ending free movement outright could also create an underclass of cheap exploitable labour. Making migrants’ lives more precarious – forcing them to take up illegal work or to be dependent on their employer for a visa – will make them more exploitable. Indeed, if the penalty for joining a trade union is to get reported for deportation, very few will organise for higher wages or better conditions.

That many communities have changed as a result of immigration and asylum is not contested, yet the benefits are also often overlooked to all our detriment. Consequently, issues that have become associated with immigration – exploitation in the workplace and social tension – are not given the scrutiny they require. To discuss them, to share concerns about change and about what it means for all involved, isn’t racist. Yet understanding such analysis isn’t the same as agreeing with the answer that immigration itself is the problem.

Quick Guide What is the EU withdrawal bill? Show What is the EU withdrawal bill? The EU Withdrawal Bill – once known as the Great Repeal Bill – is going through the House of Commons to repeal the 1972 European Communities Act and transpose all existing EU legislation into domestic UK law, which will avoid a 'cliff-edge' change on the day after we leave the EU. Parts of the bill have been highly controversial, and MPs have tabled hundreds of amendments to try and change its wording, including a significant number of Conservative rebels. Some of the key controversies include its use of so-called Henry VIII powers, which will give government ministers the power to tweak the wording of laws to make sure they make sense in UK legislation - but those changes could take place without having to go through parliament. MPs have called this a "power grab" by the government. The government estimates around 800 to 1,000 measures called statutory instruments will be required to make sure the bill is applied correctly. Other concerns include the government's decision not to include the EU charter of fundamental rights in the law being transposed. Other amendments are attempts to affect the Brexit process, including legislating for a transitional period and giving MPs a binding meaningful vote on the deal secured by Theresa May, before the deal is finalised.

Labour must champion solutions that will actually work for those left behind by decades of global economic change, social dislocation and the fragmentation of the welfare state. It will be crucial to help them learn not just one new trade, but many new skills throughout their lives. That requires increasing the resources that businesses, communities and colleges invest in training – resources that risk at present being burned up by a hard Brexit agenda focused on sacrificing everything to end free movement and cutting Britain off from Europe.

Tackling the immigration debate head on will require difficult conversations; Labour will have to have arguments with some of its own voters. Yet if the government gets its way, there could be no formal debate on free movement at all. The EU withdrawal bill, currently going through the House of Commons, will give ministers the power to scrap and create laws in relation to Brexit without a vote of the whole parliament. An amendment to the bill – number 332 – would ensure that these rights could not be undermined using those ministerial powers.

We have ample cause to demand full parliamentary scrutiny when it comes to how Britain treats refugees and migrants. This government has a disgraceful record, having already abandoned parliamentary pledges made to help child refugees, and now threatening to use Brexit as the reason to fail to uphold long established pan-European rules on reuniting families fleeing war and persecution.

The real problem we face isn’t immigration – it’s politicians themselves avoiding these questions. Labour must lead the debate on freedom of movement and ensure that we don’t forgo our obligations to those who also need us to be a place of sanctuary. We must also tackle head on the concerns about change, ensuring that resources are available, collected and effectively distributed. It is time to step up and fight for all our freedoms – regardless of where we were born.

• Stella Creasy and Catherine West are Labour MPs for Walthamstow and Hornsey & Wood Green respectively