The resignation of David Davis was about the principle of the Chequers agreement. The resignation of Boris Johnson is about ambition. But both highlight the deep political fracture that lies at the heart of Theresa May’s broken government.

The irreconcilable divide within the Conservative party over Europe has existed for more than three decades, and the appointment of new faces to the government will not change that basic fact.

Two senior cabinet resignations within a matter of hours constitutes a clear vote of no confidence in the prime minister’s Brexit strategy. However, the truth is that such a moment has been inevitable ever since May set out her hard red lines at the 2016 Conservative party conference.

After a divisive referendum, we needed a leader of leaders. Someone who could govern in the national interest. Someone who would respect the result of the referendum but develop a future vision capable of uniting the country, bringing communities back together and tackling the deep social and economic inequalities exposed by the referendum. A vision where everyone could see their future, whichever way they voted.

This is an impasse that cannot be resolved by further internal negotiation in the Conservative ​​party

Instead, May presented her party and the country with an extreme interpretation of the referendum. Rash and reckless red lines were laid down – red lines that were never compatible with securing a good deal with the European Union or speaking to a divided country. Red lines incapable of addressing the complex challenges presented by the referendum result. Red lines that could not deliver on the solemn promise of no hard border in Ireland.

The agreement struck at Chequers last Friday is flawed in many respects, but at least it appeared to be the first realisation by the prime minister that the approach she adopted two years ago was wrong. Her red lines began to yield just a bit. But even this modest shift has proved too much for some in the cabinet and the Conservative party.

Labour has consistently offered a different approach, one that is democratically legitimate, economically sensible and rooted in our country’s values. And our approach has been vindicated at every stage.

We were right to say from the outset that EU citizens should not be treated as bargaining chips but should have their rights guaranteed immediately. We were right to call on the government to publish a plan for Brexit. We were right to argue that parliament should have a proper role through the process, including a meaningful say on the final deal. We were right last summer when we made the case for a transitional period on the same basic terms as now to protect against a cliff-edge Brexit. We were right to say the UK should continue to collaborate with the EU on all areas of shared interest, from health to security. We were right to make the case for the UK to negotiate a comprehensive customs union with the EU. And we are right to argue for a strong single market deal, based on common standards, protections and regulations: the right balance of rights and obligation.

The crisis that is unfolding now is a direct consequence of a divided government. It’s an impasse that cannot be resolved by further internal negotiation in the Conservative party. Theresa May has successfully kicked the can down the road on a number of occasions, but now she has run out of road.

It is now time for the majority in parliament to be heard. It’s a majority that rejects the extreme approach to Brexit advocated by some in the Tory party. The prime minister has shown she is incapable of negotiating a way forward. She should let parliament lead the way.

• Keir Starmer is the shadow Brexit secretary