The average energy bill for households in Great Britain will rise by £111 from April to £1,849 a year for a typical household, after the energy regulator announced the third consecutive increase in the cap on gas and electricity charges.

The 6.4% rise from April largely reflects an increase in wholesale prices, and was bigger than forecasters had expected.

Ofgem last raised the cap in January by 1.2% to a rate equivalent to £1,738 a year as freezing temperatures across Europe depleted gas stores and drove market prices higher.

Campaigners said an increase in the cap would be “unbearable” for households who have struggled to pay their bills during winter.

The latest price rise means households will be forced to pay about £600 a year more for their gas and electricity than before Russia’s invasion of Ukraine three years ago.

About 9m homes that buy their energy through variable tariffs will see an immediate impact on their bills as the cap takes effect in April, while it will be delayed for others on fixed tariffs.

Households could face even higher bills if they use more than the typical amount of energy. This is because the cap, which is recalculated every three months, limits the rate energy suppliers can charge customers for each unit of gas and electricity – not the total bill.

Analysts at the energy consultancy Cornwall Insight had predicted in January that the April cap would rise to £1,785 a year, but an increase in energy market prices since pushed the figure higher. Last week, the consultancy predicted the cap would rise by £85, or 5%, from April to £1,823.

Ofgem said 11 million people are on a fixed deal and will not be affected by the change in the price cap.

Jonathan Brearley, the Ofgem chief executive, said: “We know that no price rise is ever welcome, and that the cost of energy remains a huge challenge for many households.

“But our reliance on international gas markets leads to volatile wholesale prices, and continues to drive up bills, which is why it’s more important than ever that we’re driving forward investment in a cleaner, homegrown system.”

The higher than expected price cap, which is updated every quarter, comes as a blow to the government’s election promise to bring down energy bills by “up to £300 by 2030”.

The price cap is now expected to fall slightly in the summer, according to Cornwall Insight, before rising again in October when colder weather is likely to drive household energy use higher.

Peter Smith, the policy director at the fuel poverty charity National Energy Action (NEA), said that although the price increase will take effect during spring as temperatures rise this will be “cold comfort” for many who have struggled to pay their energy bills during the winter.

“The thought of a third successive and significant price cap rise will be unbearable for many of the people we try and help. This winter has been brutal, people’s bills are already totally unaffordable, many have had less access to support and are already in unmanageable amounts of energy debt,” Smith said.

“We desperately need a more urgent plan from the government and Ofgem for supporting these vulnerable households and giving them some much needed relief with deeper support to manage their bills. Without it, what on earth do we expect these people do, how can they get by with this happening in their lives?” he added.