The company, which is due to increase its average bill by around £50 today, is thought to have made around £575 million from its domestic operation alone this year.
Centrica has blamed its rising energy bills on the costs of carbon reduction targets and upgrading the UK's gas and electricity grids, and also said it experienced a 13% rise in wholesale gas prices for this winter.
It is the second of the "big six" energy companies to announce bumper profits alongside price rises, following Scottish & Southern Energy's 38% jump in half-year profits to nearly £400m on Wednesday.
Mike Jeram, head of business and environment at trade union Unison, said: "The billion-pound profits of energy companies, announced at the same time as massive price hikes for their customers, are an insult to the many families who are struggling to get by as winter takes hold."
Audrey Gallacher, director of energy at Consumer Focus, called for rules forcing energy firms to tell customers about the link between bill rises and profits. She said: "Con-sumers will be sceptical over supplier profits, given questions over how justified recent price rises have been. It is essential all energy firms are required to provide information that is fully clear and comparable, including profit and trading information from across the whole of their business, if customer distrust is to be tackled."
The Centrica group, which makes most of its profit from upstream gas and oil exploration, provides gas and electricity to 16 million households.
An investigation is under way at Westminster over allegations energy firms manipulated the wholesale gas market in a bid to maximise their profits.
The Financial Services Authority and Ofgem are looking into the claims, which involve allegations some traders deliberately sold gas for less than the market price, although all of the UK's big six energy suppliers have denied any involvement.
Trisha McAuley, deputy director of Consumer Focus Scotland, said the suggestion that the price of gas may have been rigged was hugely damaging to consumer confidence at a time when energy companies were reporting rising profits.
She said: "Consumers have little confidence that the balance between wholesale energy costs, domestic prices and company profits is fair. The truth is that establishing whether this balance is fair has confounded regulators and Government.
"This will be the trigger to get into the guts of the wholesale gas market and its relationship to domestic prices and establish whether consumers can have confidence in the price they are being asked to pay and the increases they are expected to bear."
British Gas, which trades as Scottish Gas in Scotland, is one of five energy firms that have announced inflation-busting rises in their domestic electricity bills this year.
Of the other big six, ScottishPower announced plans to hike bills by an average 7% from December 3, Scottish & Southern put its prices up by 9% last month, while Npower plans an average rise of 8.8% for gas and 9.1% for electricity from November 26. EDF Energy will raise its domestic gas and electricity tariffs by 10.8% next month. Only E.ON has ruled out price rises this year, but it is reported to be planning bill hikes of 11% from early next year.