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British Gas say a 5% reduction in gas prices is "as much as we could as fast as we could".
Christine McGourty, Director of Corporate Affairs, said: "The 5% cut is greater than any other cut in the market so far."
The energy firm, who have benefitted from falling wholesale gas prices, will only reduce bills from the end of next month.
They were accused of "double standards" after hiking prices with immediate effect when wholesale prices rose in 2008.
ITV News Consumer Editor Chris Choi reports:
British Gas will have to live with the fact that many of their customers won't be jumping for joy over this news.
The wholesale market has been dropping for months, with wholesale costs for the next 12-month contracts down 28%.
In that context, this 5% drop can look a little bit mealy-mouthed.
The remaining big six companies that have not dropped prices yet have not given any firm signals that they will reduce prices.
If you look at when British Gas raised its prices by 35% in 2008, the new tariff came into force with immediate effect.
Today's reduction won't come in until the end of next month - some people will see that as an unfair contradiction.
Ed Miliband has said a 5% cut in British gas household prices is "too little, too late" and "not nearly enough".
"Wholesale prices have fallen by 20% so what I would say to that company and to the other companies is actually that they should pass on the benefit to consumers," Mr Miliband told voters at an event in north-west London.
"A 5% fall is too little and it is too late. It is not nearly good enough."
The Labour leader, who has proposed an energy price freeze if he is elected in May's general election, added: "If the Conservatives want a competition about who can properly stand up to the energy companies, I say bring it on.
"This Government has stood by as energy prices have gone up and up and done nothing about it."
David Cameron has told ITV News that energy suppliers like British Gas would not have cut its prices if the Government had "listened to Labour" and enforced a price freeze.
"This is excellent news and we should be absolutely clear that this price cut would not be happening if we'd listened to Labour and put in place their 20-month price freeze," the Prime Minister said after British Gas announced it was cutting household bills by 5%.
"If we'd frozen prices, you would not have got this benefit to hard-working families up and down the country who want to see their energy bills come down - and with this news, that's what is going to happen."
Labour has said the fall "is too little and too late" and "not nearly good enough" when wholesale prices have fallen by 20%.
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British Gas' decision to cut energy bills is a "further step in the right direction", Ofgem said, as it called on other companies to follow suit.
This is a further step in the right direction.
We have consistently called for suppliers to explain the growing gap between falling wholesale prices and retail prices.
Cutting prices is an explanation that consumers will understand and in a competitive market we would expect others to follow suit.
Customers from all energy companies will now be waiting for their bills to be cut after British Gas and E.on announced falls in prices, Energy Secretary Ed Davey said.
British Gas became the second of the big six energy firms to react to falling wholesale gas prices today, with the firm saying the cut would help reduce annual bills by £37 for its 6.8 million customers.
"This will be welcome news for British Gas customers - and after E.on's price cut last week, customers of other energy companies will be asking when they're going to see savings passed through," Mr Davey said.
"But while these bill cuts are welcome, the biggest savings can be made by switching to a better tariff, with many saving around £300 - or even more."
British people still "aren't getting the full benefit" of falling wholesale gas prices, Labour has said, after British Gas revealed plans to cut household bills by 5%.
Caroline Flint, the shadow energy secretary, suggested the 5% cut was underwhelming considering whole gas prices had dropped by at least 20%.
"This shows that Ed Miliband was right to challenge the energy companies to cut their prices and pass on the falls in wholesale costs to consumers," Ms Flint said.
"But given gas prices have fallen by at least 20% a price cut of just 5% means consumers still aren't getting the full benefit of falling wholesale prices."
Reacting to news that British Gas will cut its household gas prices by 5%, Prime Minister David Cameron tweeted:
It's welcome to see British Gas cutting prices. We'll continue to encourage energy firms to pass on falls in wholesale prices to customers.