Politics has rarely been so fluid. It is rare indeed for a governing party to look so vulnerable or to have made such a disastrous blunder as the Tories did in calling a snap general election.

Under these circumstances, it is the duty of Labour both to understand the social and economic background that has given rise to these conditions, and to show that it is prepared for office.

It is my privilege to have been asked by Jeremy Corbyn to lead on this task. But what should be our underlying purpose?

The party’s constitution shows the way. “We are a democratic socialist party,” it begins. And that phrase must shine like a beacon to illuminate our path. We will use the transition into government to start the task of building a socialist country, in line with the values of the British people.

At the core of this task is surely the central drive to remove the scars created by the profound inequalities in our country, which have crystallised into ossified class structures.

“Britain is a deeply divided nation.” Thus begins the government’s own Social Mobility Commission report this week. The gap between the rich and everyone else is growing at an alarming rate. While the majority of people have had to endure pay cuts, rising energy bills and increasing housing costs, the richest 1,000 have increased their wealth by £83bn in the last year and £400bn since the financial crash.

Such high levels of inequality are unsustainable, and they are at the root of the instability that characterises our political system. But this is also why, at the general election, Labour’s “for the many, not the few” manifesto resonated with so many people across Britain.

The Tories are ideologically incapable of tackling inequality. They blame the poor for their own poverty. They oversee a system that puts big money at the heart of our democracy. Lobbying, a revolving door between big business and government, and the presence of leading business people on non-executive departmental boards, have all resulted in the voices and interests of the privileged few taking priority over those of the many.

The days of such a system are surely numbered. In the short weeks of the election campaign, Labour’s message for change led to the highest share of the vote for our party since 2001.

But we cannot be complacent. The Tories, propped up by the DUP, are still in government. If Labour is to succeed at the next general election, we will need to be as ambitious as Clement Attlee when his government created the welfare state.

In 1945, the country faced a toxic mix of social malaise, similar to that felt today, and an unwillingness to go back to the 1930s. After the war, Britain faced a huge housing crisis, there was no universal healthcare and many people had no job to return to after fighting for their country. There was a choice before the whole country: to continue with politics as usual or to transform society. Labour offered the hope of socialism in the face of drastic inequality.

“Let us face the future,” was the declaration from the Labour party. Together with a radical agenda, the people chose change and voted for the first democratic socialist government.

Of course we are in a very different situation now, but there are parallels nonetheless. Perhaps the most important parallel is that we have once again a Labour leadership that is prepared to take a root-and-branch approach to Britain’s problems, rather than tinkering with their symptoms.

Nothing less will do. Timidity will not answer the deep-rooted problems that have been created by almost 40 years of neoliberalism.

Here is one of the conclusions of the Social Mobility Commission: “Tinkering with change will not do the trick. A new level of effort will be needed to tackle the phenomenon of left-behind Britain.”

Somewhere along the way, many people with a strong social conscience became convinced that a fairer Britain would have a ladder through the social hierarchy, up which anyone with talent could climb. We know that even this limited vision of fairness does not work. Here, as we approach the third decade of our new century, it is still the case that the primary determinant of how well (or badly) you do in life is class, not your talent or effort.

We now know that low social mobility is associated with great inequality. The more a society consists of a rigid hierarchy of social class, the less meritocratic it is. Labour’s goal, therefore, is surely to tackle inequality rather than the narrow pursuit of mobility. Even Anthony Crosland, the great hope of Labour’s revisionists, saw equality as our central precept.

Might a radical government therefore convert the Social Mobility Commission into a Commission for Social Equality? I would hope so.

There can be no question of complacency in our thinking. The election isn’t in the bag. We don’t even know when it will be held.

Nonetheless, it is right that we should be thinking hard now about developing an authoritative and carefully constructed model for what a Corbyn-led Labour government would look like, and how we can secure an orderly transfer into office. Such a model would indeed be a 21st-century beacon for a more just, egalitarian, modern, democratic, tolerant and outward-looking British version of our socialism.

Our manifesto was clear: we want public ownership of the utilities and railways, action on investment, to tackle the housing crisis and free education. The next Labour government needs to be ready to implement these policies and overcome any obstacles it may face.

• Jon Trickett is the Labour MP for Hemsworth