The improved figure came despite the company, the UK’s second-biggest energy supplier with brands including Scottish Hydro, losing more than 500,000 customer accounts during the year.
It blamed “increasingly challenging and highly competitive market conditions” for the decline to 8.5 million accounts.
Profits at SSE’s power plants business also continued to fall and have led to a decision to close its 1,000-megawatt Ferrybridge coal-fired power station, which employees 172 people, by March next year.
Adjusted pre-tax profits in the year to 31 March rose by 0.9 per cent to £1.56 billion.
Shareholders will receive an annual dividend of 88.4p a share, 2 per cent higher than the previous year.
SSE’s retail arm reported a 39 per cent increase in profits to £456.8m, meaning that it made an average of £69 from the supply of household electricity and gas before tax and interest payments.
The rise in profits follows a tariff hike in November 2013 and the firm’s subsequent pledge to freeze prices, which it recently extended to next summer in the wake of a 4.1 per cent average reduction in gas prices from last month.
SSE’s total customer base is now the same size as it was in 2008, having peaked at 9.65 million in March 2011.
The company also trades as Southern Electric, Swalec and Atlantic.
SSE said there are now ten suppliers of scale competing to retain and gain customers and there are a growing number of smaller players who are exempt from the cost of certain social and environmental policies.
It believes that savings for consumers worth around £100 – forecast to rise to around £200 by 2020 – could be made if such levies were not part of most energy bills.
The company said: “SSE would like to extend its price freeze again, or even cut prices if further costs can be taken out of energy supply, and will work with the new UK government or indeed any stakeholder to find such solutions.”
It said recouping the cost of social levies through energy bills takes no account of an individual’s ability to pay and is socially regressive.
The group added: “SSE has therefore continued to call for more of these levies to be moved into general taxation, making bills cheaper and fairer for those less able to pay.”
In 2014-15, SSE’s profit margin in energy supply was 4.6 per cent, compared with 2.9 per cent in 2013-14 and 4.2 per cent in 2012-13.
Energy supply profit margin has averaged 3.9 per cent over both the past five and three years.
It said customers’ use of electricity and gas is now more than 13 per cent lower than it was five years ago.
SSE said it believed that the quality of its operations, assets and investment opportunities means it can continue to deliver a full-year dividend that “at least keeps pace” with RPI inflation in 2015-16 and beyond.
The Competition and Markets Authority is currently undertaking a wide-ranging probe into the energy market to see if customers are being unfairly treated by the UK’s dominant big six energy suppliers.