Getty ImagesEnergy bills will fall in April following a shake-up in costs by the government, with details of the extent of the drop to be announced shortly.Nearly everyone in England, Wales and Scotland will benefit from a cut irrespective of their tariff, although the amounts will vary between households.Energy regulator Ofgem will publish its next price cap imminently. The latest forecasts suggest households on variable tariffs will see their bill cut by about 7%.However, prices still remain relatively high by historical standards, debts have ballooned, and billpayers are being urged to shop around for further savings.Budget promise to reduce billsDomestic gas and electricity bills are a complicated mix of charges for energy policy, costs to run the network, as well as the price of gas and electricity to run a home.In November's Budget, Chancellor Rachel Reeves announced changes to the first of these - policy costs. She said the typical annual household energy bill would fall by £150, by scrapping the Energy Company Obligation (Eco) scheme introduced by the Conservatives in government, and also moving some charges onto general taxation.However, the cost of maintaining and strengthening energy networks - including power lines, cables and gas pipes - is rising.So, analysts at the consultancy Cornwall Insight have forecast that a household using a typical amount of gas and electricity will see their annual bill drop by £117, to £1,641 in April. A similar fall was seen last summer, but prices have risen since then. The announcement for bills in April will be made at 07:00 GMT on Wednesday.Crucially, the discount on each household's individual energy bill will depend on the size and type of household and how much energy it uses.The reduction is expected to be primarily applied through a lower price per unit of electricity used. This means high electricity users, which may include vulnerable households with medical equipment, are likely to see the biggest benefit. Those who use little electricity and a lot of gas will benefit the least.Ofgem is announcing changes to its price cap, which affects millions of households on variable deals.However, the changes to policy costs will also mean a reduction in bills for those on fixed deals. They will be contacted by their supplier with details in the coming weeks on the specific change to their tariff.The wholesale cost of gas, which spiked after Russia's invasion of Ukraine four years ago and led to soaring household bills, remains relatively volatile and difficult to predict.This makes it tricky to say what will happen to domestic energy bills later in the year, but Cornwall Insight is forecasting relatively little further change.Regulators and campaigners have encouraged people to shop around for a cheaper, fixed deal, depending on their circumstances.Richard Neudegg, director of regulation at Uswitch, said: "While it is good news that the price cap is coming down, consumers should not be fooled into thinking that it is a good deal. "By moving into a competitive fixed deal, consumers could save £200 [a year] as well as get the benefit of these government changes."Cost of living pressureEnergy bills will fall in April, but other bills will increase - meaning most people will continue to face a squeeze in the cost of living.Water bills will rise sharply in some areas, council tax will go up, and various other household costs will increase. Some larger families will receive more in universal credit when the two child benefit cap is scrapped.Households struggling to make ends meet have fallen behind on energy payments, leading to a collective debt to suppliers of well over £4bn.Dhara Vyas, chief executive of Energy UK, which represents suppliers, said companies can help."They are giving them different tariffs, extra help and support, offer white goods such as efficient fridges, but they can only do this if they know who is in your household and what your circumstances are," she said.Water bills to rise again: Use our tool to find out by how muchWarmer weather hits profits at British Gas ownerMoneyPersonal financeEnergy industryCost of Living UK economy