Nick Clegg has asked the public to nominate laws and regulations they would like to see abolished.
The deputy prime minister launched a Your Freedom website, on which people will also be able to propose ways to reduce bureaucracy.
In a speech he promised "raucous, unscripted debates", which will "throw up the best ideas".
He said the "best suggestions" would be taken into account when the Freedom Bill is published in the autumn.
Nearly 350 ideas have, so far, been posted on the website - including calls to repeal the smoking ban, review speeding laws and stop the "harassment or arrest of innocent photographers" under counter-terrorism laws.
Mr Clegg, who is overseeing the coalition government's political reform programme, promised in May to create the biggest shake-up of the country's democracy since the Great Reform Act of 1832.
Proposals so far include fixed-term parliaments, an elected House of Lords and a referendum on changing the voting system.
The Your Freedom website will ask three questions including, "which current laws would you like to remove or change because they restrict your civil liberties?"
It will also ask which regulations people think should be removed or changed to make running businesses or organisations as simple as possible, and which offences people think should be removed or changed and why.
In his speech, in London, Mr Clegg said he believed the process would identify laws that make people "feel under threat" and "serve no real purpose".
Although the government would not be "duty bound" to act on popular suggestions, he said all ideas would be considered.
"Real democracy is unspun - it is the raucous, unscripted debates that always throw up the best ideas," he said.
"So be demanding about your liberty, be insistent about your rights. This is about your freedom and this is your chance to have your say."
Speaking on BBC Breakfast, Mr Clegg said there was "lots and lots of old stuff on the statute books that we should get rid of for starters".
"I've just discovered for instance, would you believe it, that there's still an old law in the statute book that says it's an offence if you don't report a grey squirrel in your own back garden," he said.
He hoped the process could lead to "maybe even a sense of fun as people think of silly rules that need to be scrapped".
At the same time, he said unnecessary laws and cumbersome regulation had a damaging effect of business.
"The key thing about this is that, whilst ministers might be able to disagree with the suggestions, the suggestions will be out there. We won't be able to control it, we won't be able to control what the most popular ideas are, what the most numerous suggestions are," he added.
A former Labour minister suggested that despite, its good intentions, the new government could meet opposition in Whitehall to the idea.
"I don't think it is a PR exercise," Lord Digby Jones said. "And to be fair to the Blair government, they tried to do a lot on it as well.
"But the problem they will come up against is that a civil servant will say to them - 'minister, you abolish this regulation and what will you do the next time someone gets hurt, because you abolished this regulation'. Turkeys don't vote for Christmas."
And while wishing the initiative well, campaign group Unlock Democracy said it had a number of concerns about the process.
"Government of all shades have done much to discredit the idea of consultation and it is crucial this does not turn into yet another cherry-picking exercise," said its deputy director Alexandra Runswick.
"Allowing people to vote and add comments online can only get you so far. The government needs to encourage a much deeper public debate which informs as well as listens in order to avoid a kneejerk response."
Repealing unnecessary laws has been a long-standing Lib Dem objective. In January Chris Huhne - who is now Energy Secretary - said Labour had created 4,200 new laws since 1997.