People buying a new home will be offered £1,000 to spend on energy efficiency and all householders will get £50 off their fuel bills under a deal over green taxes struck between the coalition parties ahead of this week's Autumn Statement.

David Cameron and Nick Clegg, whose parties have been at loggerheads over green levies, claimed that the deal would not come at any cost to the environment, despite one of the Government's key green taxes being all but scrapped.

The Energy Company Obligation (Eco), a levy on firms to help homes become more efficient, will be scaled back, leaving fewer funds better targeted at the fuel poor. The Government claims this will help cut energy bills for customers by £50, but it all depends on energy companies passing on the savings to consumers. In October, Mr Cameron infuriated the Lib Dems by announcing that he was going to "roll back" green taxes. The announcement came at PMQs, after Mr Clegg had been given less than an hour's notice.

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To allay fears by environmental groups and Lib Dems that cutting back the Eco would hamper the fight against climate change, the Tories have agreed to offset the reforms with more help for householders to be energy efficient. Mr Cameron and Mr Clegg, who said their measures carried more credibility than Ed Miliband's proposed energy price freeze until 2017, claimed the overall deal will be carbon neutral.

New homeowners will get up to £1,000 from the Government to spend on improvements to energy efficiency, alongside the existing "green deal". The money is equal to around half the stamp duty on the average house. Private landlords, schools and hospitals will also be given incentives to make their properties more energy efficient. Together, the measures will result in less carbon being used, the Prime Minister and Deputy Prime Minister said.

Any extra costs to the Government from the plans will be funded from a clampdown on tax avoidance. More details will be set out by the Chancellor, George Osborne, in his Autumn Statement this Thursday.

Support for the most vulnerable households would not change, but all help will be paid through the Warm Home Discount scheme.

In an article for The Sun on Sunday today, Mr Cameron and Mr Clegg said the Government was already helping families reduce the cost of living through freezing council tax and cuts to fuel duty and income tax. They added: "Later this week, we'll announce further help: proposals worth around £50 on average to energy bill-payers. We're doing it without taking any help from poor families or sacrificing our green commitments; and in a way that will keep Britain's lights on in the long term, too.

"Labour have promised a temporary price freeze on energy bills. But they're taking people for fools. Energy companies would hike up prices before and after the freeze – so families would end up paying more. Not only that, by cutting investment in green energy, the freeze would threaten jobs. Labour's con is the worst of all worlds. When an offer sounds too good to be true, it usually is."

Mr Cameron and Mr Clegg claimed the £1,000 for energy saving was an "all-round win: better insulation means cheaper bills; cutting carbon emissions; and boosting British businesses who provide these services".