The desperation of Theresa May and her minsters to secure a decent Brexit deal is painfully obvious to all.

Less obvious are the lengths they are prepared to go to save their political skins by cobbling together a shoddy compromise that satisfies no one.

According to the Guardian, their latest ruse is a plan to try to persuade Labour MPs to support whatever emerges from the government’s concessions in Brussels as minsters scrabble to avoid a “no deal” outcome.

My constituents in Leeds West voted to leave the EU in the 2016 referendum. I respect their decision and want to make sure they get the best possible outcome from this process.

However, there is no way I will prop up this government and rescue the prime minister by supporting their dog’s dinner of a Brexit deal that would leave my constituents and the rest of the country far worse off. No one voted to be poorer.

If ever proof were needed that those around the Conservative leadership are deluded, it is the idea that Labour MPs like me would let them off the hook by supporting a Tory hard Brexit.

We are now more than two years on from the referendum and the only certainty about the government’s Brexit deal is that it will be far worse than our current membership of the EU.

I do believe the EU needs reform. Yet the way things are heading we stand to lose all of the benefits of EU membership with none of the prizes promised by leave campaigners such as Boris Johnson and Nigel Farage.

Our vital services sector, which accounts for 80% of our economy, would be sold down the river, with businesses facing new barriers to trade with our largest market.

The impact of this would be felt in lost growth and lost jobs. Meanwhile, the most difficult decisions about our future relationship with the EU – from how to avoid a hard border in Ireland to what our trade or immigration policy should be – will be kicked into the long grass.

‘The £350 million “dividend” slogan splashed across a bus during the referendum campaign.’ Photograph: Christopher Furlong/Getty Images

This means we would be walking out the door blindfolded, with no idea where we will end up. In no way does that provide us and thousands of businesses with the certainty that we so desperately need.

We know some changes that are already happening as a result of Brexit. Food prices are rising in the shops and some firms are finding it harder to recruit workers.

As chair of the business, energy and industrial strategy committee, I have heard evidence about how drug companies are having to stockpile medicines and of the uncertainty surrounding the supply chains in the aviation and car industries.

According to some experts, Brexit is already costing taxpayers about £500m a week in lost growth. That is very different from the £350m “dividend” slogan splashed across a bus during the referendum campaign.

That is why I am supporting a “people’s vote” on the final Brexit deal. We need to ensure the people get the last word on this huge decision. By supporting a people’s vote, I am not looking to rerun the referendum. But the leave campaign did make a host of promises that we now know will not happen.

It is crystal clear the reality of what Brexit will mean is very different from what we were told in 2016.

There is far too much at stake for everyone across the country to allow a Brexit deal to be decided at Westminster alone.

If 650 MPs in Westminster get to vote on such a seismic decision affecting the future of our country, it is only fair that everyone else should play their part too.

And, if the prime minister is so confident that whatever the outcome of these negotiations will be the best deal, then she should not fear the public having the final say on proposals that will have such a massive impact on their lives.

Instead of grubbing around and trying to persuade Labour MPs to support her failed strategy, May should not be frit of a people’s vote. It is only right the public get the final say on one of the most important decisions facing Britain for decades.

• Rachel Reeves is Labour MP for Leeds West and chair of the business, energy and industrial strategy select committee