The letter, signed by Phil Bentley, managing director of British Gas, explained the company's desire to help customers keep their homes warm
It said: "For those households on the lowest incomes and finding it hardest to cope, not only have our discounted prices been held over winter, but these current 'Essentials' customers will now receive an extra £50 credit towards their winter energy bill.
"This will help around 340,000 households."
The offer will cost the company £17m, in addition to a further £20m to be invested in the company's charity, the British Gas Energy Trust, which aims to help people in debt deal with their energy bills, and help an estimated 40,000 additional homes.
British Gas increased its prices in December, broadly in line with its competitors. Yesterday (12 January), E.On raised its prices for energy by 9% for electricity and 3% for gas.
Ofgem announced an investigation into price increases at the "big six" energy suppliers – British Gas, EDF Energy, E.On, Npower, Scottish & Southern, and ScottishPower – in November.
Centrica, the parent company of British Gas, reported profits of £1.56bn in the six months to July 2010, a 65% increase on the previous year.