The boss of British Gas’s parent company was handed a pay increase of nearly 40% last year, a raise Labour attacked as “astronomical” and a “kick in the teeth” for millions of families living in fuel poverty.

Centrica chief executive Iain Conn’s remuneration jumped from £3.02m in 2015 to £4.15m in 2016, enough to pay the heating and lighting bills for nearly 4,000 customers on the company’s standard tariff.

The details of the rise come at a sensitive time for energy suppliers, just days after Theresa May said the energy market was “manifestly not working for all consumers”.

Government intervention, potentially in the form of a price cap, is seen as increasingly likely after five of the big six energy companies hiked prices. British Gas is the exception and has frozen prices until August, but experts expect the company will follow suit then because of rising cost pressures.

Much of the increase in Conn’s remuneration package is a £1.4m “recruitment award”, compensation for rewards he forfeited when he joined Centrica in January 2015 after a 29-year career at BP. He also received a recruitment award last year of £632,000. His annual cash bonus rose by £178,000 to £759,000, but his £925,000 salary remained frozen.

Centrica said it recognised the sensitivity of executive pay and was very careful to be in line with its peers. A spokeswoman said that in terms of financial performance, 2016 had been a very good year for the company, which posted an operating profit of £1.5bn, up by 4% on 2015.

Conn has said he firmly believes executive pay should be tied to performance. He told journalists last month: “When I joined the company I was asked to take a reduction in the top-end of what I could earn and also asked to take a reduction in my base pay and make sure 80% of it was performance-related. I believe the company is very responsible in this area.”

Although shareholders approved his current package, some have expressed concerns about the one-off recruitment award.

Conn, who earned £3.36m at BP in 2013, has not quite reached the heights of his predecessor at Centrica, Sam Laidlaw, who earned nearly £5m in 2012.

Unlike Laidlaw, Conn is comfortable talking to the media and has been robust in arguing against calls for a price cap in the face of rising energy bills. “A cap would almost certainly remove choice from the market,” he told the Financial Times. He has also said government intervention risked simply redirecting consumer anger from companies to ministers.

Labour reacted with anger to Conn’s pay rise, and said it was the only party able to rein in excessive boardroom pay and help those struggling to pay their energy bills.

Rebecca Long-Bailey, the shadow energy secretary, said: “Over 4 million people are living in fuel poverty across Britain so the announcement today of astronomical pay increases for certain energy company CEO’s must feel like a kick in the teeth to those families who will sit shivering tonight because they cannot afford to put on the heating. This is another clear example of the Tories’ rigged economy.”

Campaigners said the pay rise was “simply unacceptable” and showed the need for change in the market.

Emma Hughes of Switched On, a campaign to get more council-run energy companies, said: “These ridiculous pay packets are the real reason for extortionate energy bills that leave families struggling to heat their homes. Enough of these rip-off merchants.”

Mark Todd, the founder of the comparison site Energyhelpline, said he thought it was likely but not inevitable that British Gas would hike prices in August.

“In terms of Iain Conn’s salary, customers will be shocked that he received an extra 40% in 2016. The market rewards bosses that make big profits from their customers and he managed to lead the group to a £2.2bn profit in 2016,” he said.

“He gets rewarded handsomely. British Gas customers would be best to channel their anger into switching.”