Mr. Cameron said on the eve of his party conference that he would immediately begin the second phase of a "Help to Buy" program scheduled for January that provided government guarantees to banks to allow home buyers to receive mortgages with only a 5 percent down payment on properties costing up to £600,000, or about $968,000.

The government will provide £12 billion, or $19 billion, to guarantee 15 percent of a mortgage, allowing lenders to provide up to 95 percent of mortgages at reduced risk. Participants will not be allowed to use the plan to buy a second property.

Mr. Cameron announced the change in interviews with right-leaning newspapers like The Sunday Telegraph and The Sun on Sunday. He told The Sun that he wanted to put young people on the housing ladder. "The need is now," he said. "What concerns me is that you can't buy a house or a flat even if you are doing O.K., you have got decent job prospects and good earnings."

Critics say the plan may accelerate a new housing bubble, especially in London. The average cost of a house in London surged by 10 percent between July and September, compared with the third quarter of 2012, reaching £331,338, or $535,000, British bank and mortgage provider Nationwide said on Friday. The average price of a house in London, the bank said, is now 8 percent higher than in 2007, just before the global financial crisis. Across Britain, the average price of a home is £170,918, about $276,000, up 4.3 percent compared with the third quarter of 2012.

Since the mortgage guarantee part of the plan was announced in March, the rise in prices, indicating a brisk market, has raised questions about whether the plan is needed at all. Britain's business minister, Vince Cable, a Liberal Democrat, has expressed his concerns about the program, saying there was a "danger of getting into another housing bubble." And the chancellor of the Exchequer, George Osborne, last week asked the Bank of England to keep a closer eye on the impact of "Help to Buy."

Ed Balls, the Labour Party's shadow chancellor, responded on Sunday to the Cameron announcement by saying that the government should instead invest in building more affordable homes, denouncing what he said was the lowest rate of house-building since the 1920s. That was the best way for first-time buyers to get on the housing ladder, Mr. Balls said in a statement.

Mr. Cameron has also said that he would introduce tax breaks for married couples of low and medium income that could cover about one-third of married couples and civil partnerships and save them £200 ($322) a year. He said his coalition partners, the Liberal Democrats, had opposed the idea.

In his party conference last week, Labour's leader, Ed Miliband, took a more populist stand, calling for slightly higher corporate taxes and a freeze on energy prices, which the Conservatives likened to old-fashioned price controls. Mr. Cameron told The Telegraph that such policies were "nuts."

Mr. Cameron's aides were also at pains to deny reports in a new book that the prime minister and his wife, Samantha, disliked Larry, the cat who also inhabits 10 Downing Street and has high favorability ratings. Larry, 6, was adopted from a Battersea shelter in 2011 to combat a rat infestation behind the famous black door.

Mr. Cameron is trying to appeal to the right — to attract voters who favor the anti-Europe, anti-immigrant UK Independent Party — and to the center, to win back those who voted for his coalition partners, the Liberal Democrats. Elections are expected by May 2015.