The government is to follow the lead of The X Factor television programme and allow the public to decide on legislation to be put before MPs.

In an attempt to reduce what is seen as a disconnection between the public and parliament, ministers will ensure that the most popular petition on the government website Direct.gov.uk will be drafted as a bill. It is also planning to guarantee that petitions which reach a fixed level of support – most likely 100,000 signatures – will be guaranteed a Commons debate.

Ministerial sources acknowledge that the proposals have the potential to cause headaches for the coalition because populist causes célèbres – such as a return of capital punishment or withdrawal from the European Union – could come top of the list.

The leader of the Commons, Sir George Young, has signalled he wants to press ahead with government by petition in the new year.

There would be no guarantee that the government would support the most popular proposals but, subject to discussions, there would be an agreement that the issues would be converted by parliamentary draftsmen into a bill.

The e-petition reforms have the support of Downing Street strategists anxious to make politics more relevant to people's daily lives. The plans will require consultation inside parliament, and represent a fulfilment of the ideas promoted in the Conservative manifesto.

As part of the proposals, the government plans to close down the e-petition part of the Downing Street website, established in the era of Tony Blair, and reopen it in a different format on the Directgov website, so making e-petitions the responsibility of all government departments.

Efforts will also be made to ensure that those people petitioning the new website are registered voters rather than what are described as "super users", the kind of people that repeatedly back a petition on an issue.

The government is also looking at how petitions can be converted on to Facebook and other social media sites so petitioners can keep in touch with one another as they campaign for a particular issue to be taken up either by ministers or backbenchers.

One Whitehall source said: "We applaud the principle of the old No 10 website, but it became a not very edifying way to promote some particular issues rather than really lobby the government or reflect public opinion.

"We hope to have found a more efficient and mature way for the public to engage with government and parliament."

The idea that the petition with the most support will be turned into a bill is probably the most radical attempt so far to give the public greater direct access to parliament. There had been suggestions at one point that a petition would require a million signatures before it could be considered for legislation, but government sources said they recognised this large minimum threshold was unrealistic.

The government source said: "It may well mean that we see some difficult issues raised, such as withdrawal from the European Union, but that would put the onus on parliamentarians to convince one another of the many benefits of staying inside the European Union. You would have to win the argument."

There might also be difficulties about proposals that breached human rights law, were deemed impractical or had already been recently discussed by parliament.

Government sources said they were looking at ways in which the newly elected backbench business committee might be given responsibility for ensuring a bill found a sponsor, as well as for ensuring e-petitions found time to be debated, either in government or backbench time.

It is likely that any petition converted to a bill would have to go through the private member's bill route, rather than be seen as a government bill.

At present it is relatively easy for a tiny minority of well-organised backbenchers to block private members' legislation, but the all-party procedure committee has been looking to reform the system so that majority opinion in the Commons can force a bill on to the statute book.

The procedure committee in the 2008-9 session had looked at introducing an e-petition system in the Commons, but the cost was put at close to £5m, deemed to be prohibitive at a time when parliament's budget was due to be cut by 17%.

Under the old Downing Street petitioning system set up by Blair's strategic communications unit, anyone who signed a petition that reached more than 500 signatures by the time it closed would be sent a government response by email. The most popular – with 1.8m signatures – was a call for the scrapping of "the planned vehicle tracking and road pricing policy." A one-word petition calling for the prime minister to resign received more than 70,000 signatures, with only a slightly smaller number calling for him to be replaced by Jeremy Clarkson.