Total consumer energy supply customer accounts fell 6.6% to 24.4 million, while in the business segment it fell 5.9% to 1.3 million.
The British Gas owner is a junior partner to EDF Energy, the French group that operates Britain's eight nuclear reactors.
Centrica said the job losses, which are part of an extended cost-cutting programme, would fall mainly in its United Kingdom energy supply business.
Meanwhile, the firm's British Gas business shed 9 per cent of its United Kingdom domestic customers last year.The company's United Kingdom business division also saw profits plunge by 92 per cent in adjusted operating profit for the year to 31 December.
But, it said, it expects to create around 1,000 new positions as it pivots towards customer-facing operations rather than an energy supplier.
But axing 4,000 jobs, at least 2,000 in the United Kingdom, seems an increasingly desperate move to achieve such savings, and shore up investor confidence in future dividends.
Centrica, which lost a total of 1.4 million customer accounts past year, is also looking to sell its stake in Britain's nuclear power stations by 2020.
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In addition, there have been concerns over losing customers to digital services.
The company also faces a new energy force in the form of the merged npower and SSE, as well as new entrants with financial muscle such as Shell, which bought First Utility past year.
Conn refused to rule out further job losses under the cost-cutting plan, which has now been increased by £500m annually.
"We regret this deeply, and I am determined to restore shareholder value and confidence", said Iain Conn. "We're not in a blame game here".
It blamed a number of factors for the move - including pointing the finger at the government's energy price cap. Conn said it moved 700,000 customers from its SVT onto fixed price deals previous year and will do the same for another 1.3 million customers in 2018, putting the supplier in a good position to cope with the price cap.
"With so many smaller up and coming companies snapping at their heels for a larger chunk of the market, British Gas have got their work cut out if they're going to remain a key player in a competitive industry", she said.