Life has become pretty normal for most people in Northern Ireland over the past 20 years or so. Like anyone else in the UK, people go to jobs near to them or in the next town. They go to doctors, chemists and hospitals near to them. They buy local fresh food. They use trains, buses and roads to get around.

But if we in Britain get Brexit wrong, our friends in Northern Ireland will find all of these things harder to do. Why? Because of the border with Ireland, which is crossed 110 million times a year as people on either side go about their daily lives.

People live on one side of that border and work on the other. Because of European Union rules that the UK helped make, cancer care and ambulance services are run jointly across that border. You can get a prescription on one side and your medicines on the other because of more EU rules we share. Cheaper energy and more choice across Ireland is there – again, thanks to those common rules.

Most vital of all is that these things all add up to making life feel normal, when just 20 years ago the Good Friday agreement all but finished the violence and murder which killed thousands of people, including many in Britain. The border being invisible today is a big part of that peace process. We can’t let Northern Ireland go backwards by putting up any new barriers.

We don’t believe the prime minister’s Brexit deal is in the best interests of anyone in the UK, and we will vote against it. But as former secretaries of state for Northern Ireland, we do believe that if Brexit really has to happen, there must be a deal – and that no deal is reckless madness.

Nowhere is this more important than in Northern Ireland. So while we oppose Theresa May’s deal, we cannot and will not join those attacking what is known as the backstop.

Backstop seems a bad word now to some, but it shouldn’t be. It’s an insurance policy, a rainy-day backup plan in case a new UK-EU trade deal isn’t ready by the end of 2020 – or beyond. It is a sensible policy to be used only if needed (and everyone hopes it won’t be) to ensure the border between Northern Ireland and Ireland remains open and invisible.

‘Twenty years ago the Good Friday agreement all but finished the violence and murder which killed thousands of people, including many in Britain.’ Photograph: Dan Chung/The Guardian

The UK and Irish governments, along with the EU, were right to prioritise the Irish border in the Brexit negotiations. Our UK parliament has rightly focused on it too, setting in the EU Withdrawal Act a firm commitment to no new border infrastructure.

Any Brexit deal of any kind must include this insurance policy or backstop. It’s not just that Ireland or the EU won’t accept it any other way; we in the UK shouldn’t either.

It is such a pity so many politicians and journalists have become obsessed by words like “backstop”, taking away from the fact that this is about people, their lives and their livelihoods. A little-noticed document published in December by the Department for Exiting the European Union lists no less than 157 different areas of cross-border work and co-operation in Ireland, north and south, many of these facilitated by EU laws. They include food safety, tourism, schools, colleges, farming, fighting crime, tackling environmental pollution, water quality and supply, waste management, blood transfusions and so on.

Whatever happens with Brexit, it is vital we protect what we’ve achieved in Northern Ireland together in the last 20-30 years – and avoid any hardening of the border in any way. When parliament returns from the Christmas recess on Monday, we call on our fellow politicians, including the DUP, to stop playing politics with Northern Ireland and insist on an insurance policy over the border.

• Paul Murphy and Peter Hain served as secretaries of state for Northern Ireland successively between 2002 and 2007