leader Nick Clegg has revealed plans to give cities and regions a legal right to home rule - with draft laws due to be published in January.
Speaking to the Birmingham Post during the party's annual conference in Glasgow, Mr Clegg set out proposals to introduce "devolution on demand" for English local authorities, by giving them the legal right to demand more powers from central government.
also spoke about his plans for an English and Welsh "Grand Committee" in the Commons - with membership chosen through proportional representation.
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He backed Government plans to fight extremism in schools, and warned councils weren't doing enough to deal with the problem.
And he accused his Coalition allies of setting out plans to cut public services "to the bone" if they govern alone after the next election.
The "devolution on demand" plan is Mr Clegg's response to calls for the English regions to be granted more autonomy, following promises of greater devolution to Scotland made by all the major parties during the Scottish independence referendum campaign.
He said: "One of the lessons I have learned in government, and of course it is an observation which has been given even greater force after the Scottish referendum, is the desperate need to decentralise power from London to other parts of England. It really is the missing bit of the constitutional jigsaw.
"As more powers are devolved to Scotland in what is in effect home rule to Scotland – and I also hope we start delivering home rule in Wales and there is a debate about whether we devolve further tax powers to Northern Ireland – the missing bit of the jigsaw which is how power is still so firmly hoarded in London.
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"What I am working up at the moment is ideas on how we can enshrine in law a statutory right for local areas, whether it is the North West, the North East, the South West – wherever it is, to demand new powers from Whitehall.
"In other words to take down new powers from Whitehall and enshrine that right, that sort of devolution on demand, in law, which can only be refused if there are very very good reasons."
The measures would change the relationship between local authorities and Whitehall. Instead of councils asking the Government for autonomy, they would be able to demand it and central government could only refuse if there was a specific reason for doing so.
Authorities in the past have sought more control over skills, economic development, transport decisions and housing.
Mr Clegg's proposals do not specify which bodies would exercise greater powers but it is likely that combined authorities, bringing together a number of neighbouring councils, would take the lead.
The Lib Dem leader said he wanted to move quickly, although it is not clear whether his proposals will be accepted by his Conservative coalition partners.
He said: "I very much hope, there is a lot of technical work still to be completed, but I very much hope we could publish some draft legislative articles on that on roughly the same timetable as we will be publishing the draft articles on devolution to Scotland at the beginning of the year."
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Devolution to English regions and cities would have to include giving them more power to raise their own funds, he said.
"This dependency culture that we have almost of our great communities and big cities having to go cap in hand to politicians and civil servants in Whitehall is really not healthy.
"It was taken to excess under the years. Everybody realises you can't run a country as big and complex as ours from London.
"If you look at the great achievements of our cities in the past – the industrial revolution, the Birmingham of Chamberlain and others, cities which were able to raise their own money and spend it to a much greater extent than is the case now."
The Liberal Democrat leader also has an answer to the question of whether Scottish MPs should be allowed to vote on English issues in Parliament – and it involves introducing proportional representation, a traditional Lib Dem cause, in the House of Commons.
He wants to create a Grand Committee of English or English and Welsh MPs with the power to veto legislation which affected only England or England and Wales.
The Commons as a whole would continue to pass laws as it does now.
And Mr Clegg wants the committee's membership to reflect the number of votes received by each party.
This is a break with Commons tradition, as seats on committees are usually allocated to each party based on the proportion of seats they have in the house as a whole.
Mr Clegg's proposal would effectively introduce proportional representation into the Commons. He said it was essential, because otherwise Conservatives would dominate the Grand Committee.
He said: "It's terribly important that is done in a way that reflects the votes cast for each party in England and Wales and it's not used as a ruse by the Conservatives to basically stitch up Westminster because they have a majority of English MPs even though they won 38 per cent of the vote."
He added: "It wouldn't survive very long if people very quickly worked out that if you did it in the way I think is being proposed by the Conservatives it's actually just a rather grubby game by one party to get one over on the others."
Mr Clegg said he backed proposals set out by Theresa May, the Conservative Home Secretary, to launch a new campaign against extremism following the "Trojan Horse" affair in Birmingham, when a group of school governors attempted to impose a narrow Islamic ideology on schools.
A previous campaign, called Prevent, had focused on combating extremism which encouraged terrorism or violence, but the Government's new scheme is supposed to combat intolerance of all descriptions.
Mr Clegg said he also wanted to see local education authorities given a legal duty to look out for and oppose extremism in schools.
He said: "One thing we are looking at and I think we should do is putting programmes like Prevent on a statutory footing so that local authorities are duty bound to play their part.
"Because you can't be effective in dealing with extremism unless local government and central government pull in the same direction.
"But there have been quite a lot of instances where some parts of the local government family aren't pulling their weight as much as others.
"And that's why it is sensible to put it on a statutory footing."
In his speech to the Liberal Democrat conference, Mr Clegg argued that Labour could not be trusted with the economy - but Conservatives were happy to hammer the poor
However, he said he agreed with the other two parties that more spending cuts were needed and admitted some of these would come from benefit cuts, although he also said he favoured higher taxes on the rich.
Liberal Democrats are proposing a new property tax on the most expensive homes.
"I have never hidden that we have made considerable welfare savings around £18 billion, and we will need to make more."
But he said he was "angry" with proposals to freeze benefits for two years set out by George Osborne, the Chancellor, in his speech to the Conservative conference.
"In ruling out any changes to the benefits given to wealthy pensioners, in ruling out any contribution from his big donors, the very wealthy in this country, through even a penny of extra taxation, you place even more of a burden on the working poor.
"And you place massive strain on many of the public services that many people in this country rely upon.
"If you promise the huge unfunded tax cuts that they are, claim you are going to protect spending for the NHS, refuse to ask your wealthy mates to pay any extra in tax, you know what will happen - your local police forces, local social care homes, your schools, will be cut to the bone."