Britain is divided and insecure. Years of destructive austerity and a broken economic model have delivered a country of job insecurity, shortages of affordable housing, agency working, wage undercutting and gaping inequalities.

Since voters decided to leave the European Union, those divisions have grown wider. There has been a spike in racist and xenophobic incidents. Many remain voters feel shellshocked and alienated from those who backed leave. The country now faces economic and political crisis. The government is in disarray. As Labour demanded, George Osborne has had to drop his plan for a job-destroying budget surplus. But none of those seeking to replace David Cameron has any kind of exit plan. Instead, once again, they are planning to make working people pay, with yet more spending cuts and tax rises.

What’s needed instead is leadership and a clear strategy. We must respect the democratic decision of the British people – and negotiate a new relationship with the EU: one that protects jobs, living standards and workers’ rights – and also ensures we have the freedom to reshape a 21st century economy for all our people.

To bring the country back together, we have to understand what lay behind the narrow majority to leave. Part of it was clearly about the impact of immigration on a deregulated jobs market and investment-starved housing and public services.

But leave voters were also concentrated in former industrial areas hit hardest by low pay, job insecurity and economic stagnation. In fact, Labour-supporting cities that voted remain, such as London, Bristol and Manchester, have far higher migrant populations than many that backed leave.

The difference is that the latter are areas that have benefited least from a lopsided economic recovery. This was a vote by the people of left-behind Britain against a political establishment that has failed them.

Labour campaigned to “remain and reform” the European Union, and two-thirds of Labour supporters voted remain. That gives us a strong basis to bring together voters from both sides – and set a progressive agenda for negotiations that reflect the needs of the majority. The starting point has to be the red lines laid out by Labour’s shadow chancellor, John McDonnell: including the maintenance of existing employment and social rights, freedom of trade with Europe, and protection of work and residency rights for both EU citizens in Britain and British citizens in Europe.

This week Labour overwhelmingly won a vote in the Commons, led by our shadow home secretary, Andy Burnham, calling on the government to commit to giving EU nationals in the UK the right to remain.

But we need to go further. During the referendum campaign, we argued for an end to EU-enforced liberalisation and privatisation of public services – and for freedom for public enterprise and public investment, now restricted by EU treaties. Those freedoms need to be part of the coming negotiations. Labour also campaigned for tougher regulation of the jobs market and of the exploitation of migrant labour to undercut pay and conditions, as the best way to protect jobs and living standards in the EU.

The same goes for Britain outside the EU. If freedom of movement means the freedom to exploit cheap labour in a race to the bottom, it will never be accepted in any future relationship with Europe. But the reality is that we have allies in that cause across Europe, as on many other issues that will be at the heart of the negotiations ahead. Those negotiations cannot be left to a Tory government that does not speak for the country.

That’s why I am meeting fellow European socialist leaders in Paris this week to discuss the refugee crisis and Europe’s future after Britain’s vote to leave. The increasing momentum to reform the EU will strengthen the Labour case.

Politics has changed for good. After years of disastrous wars, ballooning inequality and a failing political elite, there can be no more business as usual. The damning verdict of the Chilcot report on the Iraq war confirmed that while the political establishment got it disastrously wrong, the majority of our people called it right. This political sea-change is also what led to my own election nine months ago, by 60% of Labour members and supporters.

I have made clear I am ready to reach out to Labour MPs who oppose my leadership

During that time, we have repeatedly forced the government to drop damaging policies, won every byelection, and beaten the Tories in the local elections. I have made clear I am ready to reach out to Labour MPs who oppose my leadership – and work with the whole party to provide the alternative the country needs. That’s why I am pleased that trade union leaders are exploring ways to bridge the gap and work together more effectively. But MPs also need to respect the democracy of our party and the views of Labour’s membership, which has increased by more than 100,000 to over half a million in the past fortnight alone – by far the largest it has ever been in modern times.

Our priority must now be to mobilise this astonishing new force in politics, and ensure people in Britain have a real political alternative. Those who want to challenge my leadership are free to do so in a democratic contest, in which I will be a candidate.

But the responsibility of our whole party is to stand up in united opposition to the Tory government. If we come together, we can take them on and win.

• The photograph on this article was changed on 8 July 2016. The earlier photograph showed boarded-up houses in Liverpool, and had a caption implying that the city had a majority of leave voters. In fact more than 58% in the city voted remain