 HOUSEHOLD energy bills will rise by more than ?300 a year as a result of the Coalition's green policies, a senior Downing Street adviser has told David Cameron.  The Prime Minister has been warned that government plans to get people to reduce their bills through efficiency measures are likely to fail.  Mr Cameron's senior energy adviser pours scorn on claims by Chris Huhne, the Energy Secretary, that rises in gas and oil prices will be offset by people using less power. a note by the adviser describes his department's analysis as "unconvincing".  It warns that the Government's move to increased nuclear power, wind turbines and other measures will add 30 per cent to the average family's annual energy bill of ?1,069 by the end of the decade.  Mr Cameron is said to be "very worried" about the figures in the paper, written by Ben Moxham, his senior energy adviser who was recently brought in to beef up the Prime Minister's policy unit.  The private note, seen by The Daily Telegraph, is titled "Impact of our energy and climate policies on consumer energy bills". It was sent to Mr Cameron and offers a blunt assessment of how Coalition energy plans, in particular a series of green policies, will affect householders.  It concludes: "Over time it is clear that the impact of our policies on consumer bills will become significantly greater."  Rising energy bills represent a problem for the Coalition at a time when wages are being squeezed and inflation is high.  Mr Cameron has vowed to bring down energy prices by giving the regulator Ofgem tougher powers, but this year he has had to watch as energy companies increase their prices. The disclosure that Mr  Cameron's own policies are likely to add "significantly" to the burden on householders will anger voters. Just two months ago, Mr Huhne described calculations by researchers at Cambridge University that the Coalition's reforms would increase bills by 32 per cent as "rubbish".  The six-page document, dated July 29, says: "DECC's [Department of Energy and Climate Change] mid-case gas price scenario sees policies adding 30 per cent to consumer energy bills by 2020."  The report then identifies four policies that it says will increase bills, including the Government's demand for energy to come from more renewable sources and the plan to guarantee power companies a fixed price for electricity if they use low carbon methods to generate it. The paper, addressed to the Prime Minister, is copied to just 12 of his No10 aides, including Jeremy Heywood, his permanent secretary, Ed Llewellyn, his chief of staff, 