VAT will be cut from household electricity bills, the government has announced, as part of new prime minister Andy Burnham's pledge to help with the cost of living.

The reduction from 5% VAT will come into effect on 1 October, saving a typical household about £45 a year.

Ministers said it would be funded by savings from the cancellation of the digital ID programme, which was going to cost £1.8bn over the next three years. The government estimated it will cost £850m this financial year.

John Healey, the new chancellor, said that the announcement would "provide some reassurance this winter".

Suppliers have been told the VAT reduction should be passed on to all household customers, including those on fixed tariffs, as was the case when some charges were taken off bills in April.

The cut will take effect in England, Scotland and Wales, but equivalent funding would be given to Northern Ireland, which is regulated differently, the government said.

Small businesses who qualify for the domestic energy VAT relief and are not registered for VAT, as well as charities and residential care homes eligible for the reduced rate, will also benefit.

Cutting VAT is a relatively basic tool to reduce an energy bill – with larger households likely to save more as they use more electricity.

However, some vulnerable households are also high electricity users, such as for running medical equipment.

Household energy prices rose by 13% for millions of people in England, Scotland and Wales at the start of July, under regulator Ofgem's price cap.

Price rises were driven by the higher cost of gas, but have a relatively limited impact owing to warm weather and lower energy use during the summer months.

However, higher energy prices caused by the US-Israeli war with Iran, which has constrained global supplies of oil and liquified natural gas, are likely to persist into the winter, according to analysts.

In his first speech as the UK's prime minister, Burnham vowed to provide "breathing space" for households struggling with the cost of living.

On Tuesday, he said the VAT cut would "put more money in people's pockets".

The VAT cut is the second intervention on energy bills by the government in six months.

Former chancellor Rachel Reeves removed one levy and shifted others onto general taxation to lower bills in April.

Burnham's new cabinet is due to meet for the first time at lunchtime on Tuesday.