David Cameron declared yesterday he wanted his vision of a "big society" of community work and social enterprise to be one of the "great legacies" of his government.

The Prime Minister set out his plans alongside Deputy Prime Minister Nick Clegg, in their first joint public engagement since their press conference last week.

Mr Clegg, the Liberal Democrat leader, strongly criticised the Tories' "big society" proposals during the election campaign.

But he attempted to smooth over any differences on the issue yesterday, saying he had come to discover that the two parties had been using "different words" that meant "the same thing".

The coalition partners were speaking to community leaders invited from across the country to a meeting around the Cabinet table in Number 10.

The government yesterday published its proposals on civil society as the first chapter of a more comprehensive coalition agreement document.

Mr Cameron said: "It's a big signal that the first part to be published is actually that part about having a big society, decentralising power, about empowering communities, about all the work you do to help build the big strong society you want to see in the United Kingdom.

"I hope this is the start of something very big."

He said he wanted a shift away from politicians sitting around the table they were at, "telling us all what to do, issuing orders and instructions and passing laws and regulations".

He said he did not have "some naïve view" that the "big society" would spring up in the place of cuts in government spending.

But he said he was determined to help social enterprises and community-minded groups and individuals to do what they could.

"It's something I would like to be one of the great legacies of this government, to build the big society," he said.

"Yes, we have to deal with the deficit, yes we have to make sure we secure the future in Afghanistan and bring the troops home.

"But to me personally what I would most like to be a legacy is actually helping build the big society and the work that all of you and many hundreds of thousands of people in the country do."

Mr Clegg told community leaders that the fact that yesterday's meeting was taking place so early in the new government was "expression I hope enough of how much importance we together in this new coalition government attach to what you do".

He went on: "What I'm discovering is we've been using different words for a long time - it actually means the same thing.

"Liberalism, big society. Empowerment, responsibility. It means the same thing.

"I think what we are grappling with is nothing less than a huge cultural shift where people in their communities, in their homes, on their street, don't always turn to answers from officialdom, from government, but they feel both free and empowered to help themselves and help their communities."

His comments struck a distinctly different note to those he was making during the election campaign.

In one pre-election interview, on May 2, Mr Clegg said: "What is this big society? It is a big society with a price tag attached.

"It's a bit like inviting someone to a party in a pub and finding that it's your card behind the bar paying for everyone's drinks."

The gathering took place after the Cabinet met, for just the second time since last week's coalition was formed, yesterday morning.

The Prime Minister told the Cabinet that their focus this week would be on finalising the government's programme of legislation ahead of the Queen's Speech next Tuesday.

"This would be built around the themes of freedom, fairness and responsibility and would reflect the government's priorities of deficit reduction, political and public service reform," the Prime Minister's official spokesman said.

The Cabinet also discussed work to find £6 billion of cuts in departmental spending - ahead of an announcement by Chancellor George Osborne on Monday - and the "big society" agenda.

It received updates on the impact of volcanic ash on UK flights and the situation in violence-hit Thailand, while Foreign Secretary William Hague reported back on his trips to the US and Madrid.

The Cabinet Office released a document, entitled Building the Big Society, detailing the plans that the Tories and Lib Dems have agreed as part of the coalition.

They included:

• Reforming the planning system to give neighbourhoods more power over their areas and giving communities the power to take over local state-run services;

• Encouraging volunteering, with the creation of a new "Big Society Day" and appraising civil servants on their community involvement;

• Introducing a National Citizen Service for 16-year-olds;

• Giving greater financial autonomy and a general power of competence to local authorities;

• Supporting charities, social enterprises, mutuals and co-operatives that want to run public services, and allowing public sector workers to take over their services;

• Using money from dormant bank accounts to set up a "Big Society Bank" to finance neighbourhood groups, charities, social enterprises and other non-governmental bodies;

• Creating a new "right" to government data and requiring the police to publish detailed local crime statistics every month.

The document stated: "Building this Big Society isn't just the responsibility of just one or two departments.

"It is the responsibility of every department of government, and the responsibility of every citizen too. Government on its own cannot fix every problem. We are all in this together.

"We need to draw on the skills and expertise of people across the country as we respond to the social, political and economic challenges Britain faces."

Dame Margaret Eaton, chairman of the Local Government Association (LGA), said it was "good news" that the government had listened to its call for a general power of competence for councils.

"This will deliver better results for communities and citizens will truly believe their vote matters, helping to create a more vibrant local democracy," she said.

"National politicians have called for a 'new politics' that is closer to voters and brings them closer to the people they serve. Locally elected councillors are already practising it.

"We believe a radical devolution of power to local authorities will deliver big savings to the taxpayer and help make vital services even more responsive to people's needs."

But Sir Jeremy Beecham, leader of the LGA Labour group, said the government had "effectively bypassed local government" at today's event.

"While announcing that councils would be given a general power of competence, it's striking that no representative of the LGA was invited to No 10 alongside representatives of voluntary and community groups," he said.