Mr Cameron says the Tories still face an uphill task
David Cameron has said he is not taking victory at the election for granted, saying the public are going to take "a lot of convincing" to elect the Tories.
The Conservative leader told Absolute Radio that "everything has to go right" for his party to win a majority after a decade in opposition.
This came as a ComRes poll suggests the Tories have an 18-point lead.
Business Secretary Lord Mandelson has said Labour is now the "underdog" and will find it difficult to keep power.
The ComRes poll, in the Independent, suggests the Conservatives have a 42% share of the vote, up six points on last month, with Labour on 24% and the Liberal Democrats on 18%.
If this result were replicated at the election, ComRes suggests, it would give Mr Cameron a majority of more than 150.
But the Conservative leader said victory was "absolutely not in the bag" and that the Tories still faced an uphill task.
"Margaret Thatcher had to win 40 seats to get a majority, just to win. We need to win 120 seats. Everything has got to go right."
The public wanted to see the opposition had plans in place to deal with the challenges facing the country and in particular, would be "safe and sensible on the big economic decisions".
"They are going to take a lot of convincing."
Mr Cameron added: "We are really focused on what we need to do between now and the next election. I really don't take it for granted."
Mr Cameron will begin his summer break with a family holiday in France next week and is due to take a further break in Greece later in August.
While he is away, he said he would delegate responsibility to a number of "senior figures" in the party such as William Hague, George Osborne, Ken Clarke and Chris Grayling.
The Tories confirmed that Mr Hague, the shadow foreign secretary, would nominally be in charge over the period, "working closely" with senior colleagues.
Meanwhile, the Conservatives have come under fresh attack over their new alliance in the European Parliament.
Jewish leaders and anti-racism groups have alleged that Michael Kaminski, the chairman of the new European Conservative and Reformist group of MEPs which Conservatives MEPs joined earlier this month, once had links to far-right and Neo-Nazi groups.
But Timothy Kirkhope, Conservative leader in Brussels, said the allegations against Mr Kaminski were "complete nonsense" and politically motivated.
The Tories' decision to withdraw from the European People's Party (EPP), home to French, German, Spanish and Italian MEPs, after June's euro elections has proved controversial.
Labour and the Lib Dems say it has consigned the Conservatives to the margins of Europe but the Tories say the EPP is a federalist group and their new partners are mainstream parties in central and eastern Europe.