Plans to hold a referendum on changes to the voting system on the day of the next general election are being considered in Downing Street as part of a ploy to expose David Cameron as a roadblock to sweeping constitutional reform.

The idea, backed by senior ministers, has come to light amid growing recriminations within the Labour party over poor campaign strategy and a lack of fresh ideas for attacking Cameron, following Labour's thumping loss in Thursday's Norwich North byelection.

Last night, after the Conservatives overturned a 5,000 Labour majority to win the Norwich seat by 7,348 votes, Labour MPs gave warning that, unless the party did more than peddle scare stories about possible Tory spending cuts, it faced a wipeout at the next election.

Cabinet sources have revealed that one idea being developed is to paint Cameron as a leader opposed to a wide-ranging reform of the political system that voters are demanding following the scandal over MPs' expenses.

As part of this, plans are being considered to hold a referendum on general election day in which people would be asked to support or reject a switch from the present first-past-the-post system to a new model, under which candidates would need to have the support of at least 50% of voters to be elected.

If a majority backed change, a new method of voting called Alternative Vote (AV) could then be introduced at the election after next. Critics say first-past-the-post is unfair as it does not reward smaller parties in relation to their share of the vote and ensures the two main parties hold a virtual duopoly on power.

Government insiders say the plan would be a step towards fairer voting. But they also believe it has tactical attractions as it would force Cameron, a staunch supporter of first-past-the-post, to campaign actively against change and for a "no" vote ahead of an election.

A senior minister told the Observer: "This is around as an idea, although nothing has been decided. It is the kind of thing that could firm up in the months to come."

Another source said: "It has the added attraction that if the Tories won power and the answer in the referendum was 'yes', the first act of a Cameron government would be to do something he was fundamentally opposed to, or overturn the will of the people."

Gordon Brown has made clear that he is against a move to full proportional representation, because he does not want to break the link between MPs and their constituents. The AV system, however, would retain that link. Instead of simply marking an X on the ballot paper, voters would rank candidates on offer. If no one candidate gained a majority of first-preference votes, second preferences of the candidate who came last on the first ballot would be redistributed until someone reached the 50% threshold. Cabinet ministers favouring some form of change include Alan Johnson, Peter Hain, John Denham and Ben Bradshaw.

Willie Sullivan, from Vote for a Change, said the government had three months to show it was serious. A referendum would require legislation in November's Queen's speech.

"If we are going to restore faith in politics, we need more than tinkering," he said. "The public expect a big bang reform, untainted by vested interests or political calculation. We need reform that puts the voters back in the driving seat. That means giving people a choice on whether or not we keep safe seats, jobs for life and the cheap theatre that passes for debate in our parliament."

Last night Kate Hoey, the Labour MP for Vauxhall, said she was shocked by her party's campaign in Norwich. "It was very negative, all about Tory spending cuts and stuff that frankly people did not believe. We have to do better than that to stand any chance at the next election."

One senior Labour MP, Barry Sheerman, called Brown's leadership into question, saying that the prime minister needed to reconnect with the public by the end of the summer.

"We've got to get our act together, and to get your act together you don't go away for the summer and hope this all blows over," he told BBC Radio 4's Today programme. "The fact of the matter is we've got to think about how a party in government renews itself, how it does that. It's partly a question of leadership, it's partly a question of ideas."