"We expected the new programme to involve reduction in like-for-like headcount of around 4,000 by 2020," the company, which employs around 33,000 people, said in a statement.
Centrica chief executive Iain Conn said the company's financial result for the year had been "weak" and put the blame partly on the possibility of a price cap being introduced in Britain.
"There is a link between our cost efficiency programme and preparing for any price cap in the UK. We've got to be competitive and this measure means we've got to drive more efficiency," Conn told the BBC.
In a statement Conn blamed the results on "political and regulatory intervention in the UK energy market, concerns over the loss of energy customers in the UK and the performance issue in North America".
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The company said the total number for account holders in Britain had fallen to 20.34 million from 21.72 million over the year -- a decline of 6.0 per cent.
The number in North America went down by 9.0 per cent.
Centrica, which owns British Gas, said its operational profits had fallen 17 per cent to 1.25 billion pound (1.41 billion euros, USD 1.74 billion).