David Cameron has told the BBC he will not serve a third term as prime minister if the Conservatives remain in government after the general election.

The PM said if re-elected he would serve the full five years of another Parliament and then leave Number 10.

Cameron tipped Home Secretary Theresa May, Chancellor George Osborne and London Mayor Boris Johnson as potential successors.

Labour accused him of arrogance while the Lib Dems called him presumptuous.

In an interview with BBC deputy political editor James Landale, Cameron described the three Conservative heavyweights as "great people" with "plenty of talent".

'Shredded Wheat'

James Landale said the PM's comments would "electrify the election campaign".

"Not only will this kick-start a lengthy Tory leadership contest, it will also send a message to voters that if they back the prime minister now, he would not go on and on as some previous prime ministers had done," he said.

"But it is quite a gamble. There is a risk that some voters will think Cameron is being arrogant for presuming the result of an election that could see him dismissed from Downing Street in a matter of weeks."

The prime minister said during the interview he felt his job was "half done" with the economy "turned round" and that he wanted to "finish the job" of education and welfare reform.

But he said: "There definitely comes a time where a fresh pair of eyes and fresh leadership would be good, and the Conservative Party has got some great people coming up - the Theresa Mays, and the George Osbornes, and the Boris Johnsons.

"You know, there's plenty of talent there. I'm surrounded by very good people."

He added: "I've said I'll stand for a full second term, but I think after that it will be time for new leadership.

"Terms are like Shredded Wheat - two are wonderful but three might just be too many."

Asked whether he could imagine "life outside" if he falls short at the election, Mr Cameron said one day he would "find something else to do" and that he hoped to continue being an MP.

Labour said Cameron was "taking the British public for granted" by discussing a third term.

Shadow foreign secretary Douglas Alexander, the party's general election co-ordinator, said: "It is typically arrogant of David Cameron to presume a third Tory term in 2020 before the British public have been given the chance to have their say in this election."

A UKIP spokesman said: "Cameron's announcement will create the long-awaited civil war in the Conservative Party over Europe."

The Liberal Democrats described the prime minister's comments as "incredibly presumptuous".

But Johnson played down the significance of his remarks. "Frankly it really is people making a fuss about nothing," he said.

Speaking on BBC Newsnight, Conservative Chief Whip Michael Gove said the comment had been a "statement of the bleeding obvious".

"The prime minister was asked a direct question and he gave an honest answer," he added.

'Sanity check'

Former Labour Prime Minister Tony Blair ruled out seeking a fourth term ahead of the 2005 general election, leading to speculation about his replacement. His party won that election and Gordon Brown took over as prime minister in 2007.

Conservative Prime Minister Margaret Thatcher won a third term at the 1987 general election, but resigned in 1990 following a leadership challenge and was replaced by John Major.

Cameron was elected Conservative Party leader in 2005, and became prime minister in 2010 at the head of the coalition government with the Liberal Democrats.

He revealed his intentions in a wide-ranging interview in the latest of a BBC series looking behind the politics of the party leaders.

He also said his eldest daughter, Nancy, was campaigning to get Jeremy Clarkson reinstated as the presenter of Top Gear. Clarkson, who has been suspended following a "fracas" with a producer, is a family friend and neighbour in Cameron's Oxfordshire constituency.

The prime minister joked: "Nancy has threatened to go on hunger strike unless Jeremy Clarkson is restored. I told her this is not necessarily a useful intervention. It is not exactly Gandhi."

He also admitted that being seen as posh had made it easier for his political opponents to describe the Conservatives as a party of the rich, and described his wife Samantha as his "sanity check" during the election campaign.