The size, scope and role of government in Britain has reached a point where it is now inhibiting, not advancing the progressive aims of reducing poverty, fighting inequality, and increasing general wellbeing. Indeed, there is a worrying paradox – because of its effect on personal and social responsibility, the recent growth of the state has promoted not social solidarity, but selfishness and individualism.

But just because big government has helped atomise our society, it doesn't follow that smaller government would automatically bring us together again. A simplistic retrenchment of the state which assumes that better alternatives to state action will just spring to life unbidden is wrong. Instead we need a thoughtful reimagination of the role, as well as the size, of the state.

In the fight against poverty, inequality, social breakdown and injustice I want to move from state action to social action. But I see a powerful role for government in helping to engineer that shift.

Since the immediate postwar period, the most significant extension of the state has taken place under the current Labour government. Did the rapid expansion since 1997 succeed in tackling poverty? Did it reduce inequality? It would be churlish to deny that some progress has been made. But – quite apart from the fact that it turns out much of this has been paid for on account, creating debts that will have to be paid back by future generations – a more complete assessment of the evidence shows that, as the state continued to expand under Labour, our society became more, not less, unfair.

In the past decade, the gap between the richest and the poorest got wider. Indeed, inequality is now at a record high. The very poorest in our society got poorer – and there are more of them. And studies by the Sutton Trust indicate that social mobility has effectively stalled – people are no more likely to escape the circumstances of their birth than they were 30 years ago.

So what's the alternative? Our answer is twofold: first, making opportunity more equal – in which education plays the key role – and, second, actively helping to create a stronger, more responsible society.

Making opportunity more equal means better early-years provision for the poorest families. It means better education so if families fail, children have a second chance. And it means better adult education so people without skills can lift themselves up later in life.

An emphasis on responsibility is absolutely vital. When the welfare state was created, there was an ethos, a culture to our country – of self-improvement, of mutuality, of responsibility. You could see it in the collective culture of respect for work, parenting and aspiration. But as the state continued to expand, it took away from people more and more things that they should and could be doing for themselves, their families and their neighbours.

The big government approach has spawned multiple perverse incentives that either discourage responsibility or actively encourage irresponsibility. The paradox at the heart of big government is that by taking power and responsibility away from the individual, it has only served to individuate them. What is seen in principle as an act of social solidarity has in practice led to the greatest atomisation of our society. The once natural bonds that existed between people – of duty and responsibility – have been replaced with the synthetic bonds of the state – regulation and bureaucracy.

But just because big government has undermined our society, it does not follow that retrenchment of the state will automatically trigger its revival.

Our alternative to big government is not no government – some reheated version of ideological laissez-faire. Our alternative to big government is the big society. But we understand that the big society is not just going to spring to life on its own: we need strong and concerted government action to make it happen. We need to use the state to remake society.

The first step is to redistribute power and control from the central state and its agencies to individuals and local communities. That way, we can create the opportunity for people to take responsibility. Our plans for decentralisation are based on a simple human insight: if you give people more responsibility, they behave more responsibly. So we will take power from the central state and give it to individuals where possible – as with our school reforms that will put power directly in the hands of parents.

Where it doesn't make sense to give power directly to individuals, for example where there is a function that is collective in nature, then we will transfer power to neighbourhoods.

So our new local housing trusts will enable communities to come together, agree on the number and type of homes they want, and provide themselves with permission to expand and lead that development.

Where neighbourhood empowerment is not practical we will redistribute power to the lowest possible tier of government, and the removal of bureaucratic controls on councils will enable them to offer local people whatever services they want, in whatever way they want, with new mayors in our big cities acting as a focus for civic pride and responsibility.

How do we guarantee that the big society advances as big government retreats? By creating a new role for the state: galvanising, catalysing, prompting, encouraging and agitating for community engagement and social renewal. It must help families, individuals, charities and communities come together to solve problems. We must use the state to help stimulate social action.

The era of big government has run its course. Poverty and inequality have got worse, despite Labour's massive expansion of the state. We need new answers now, and they will only come from a bigger society, not bigger government. That's why it's now clear to me that the Conservatives, not Labour, are best placed to fight poverty in our country.

David Cameron is leader of the Conservative party. This is an edited extract from his Hugo Young lecture, delivered at Kings Place in London last night. Read a longer version, Polly Toynbee's critique, and join the debate, at theguardian.com/commentisfree