SSE has been criticised for not passing more savings on to customers after it revealed pre-tax profits of almost £549 million in the six months to September.
It means the energy giant's half-year profits are up 48% on the same period last year, thanks in part to unsettled weather in Scotland and Ireland.
uSwitch consumer policy director Ann Robinson claimed the results provided "yet more evidence" that energy suppliers in general were benefiting from lower wholesale prices, and called on SSE to make more substantial price cuts.
"Consumers are not cash cows," she said. "It is simply unacceptable that, while SSE is set to make healthy profits, many of its customers are fearing sky-high energy bills this winter.
"Wholesale prices remain at record lows, yet SSE has made only one cut to its standard gas tariff this year. It is high time for some decent, double-digit price cuts from all suppliers to both standard gas and electricity tariffs to ease the pain of exorbitant bills."
SSE chief executive Alistair Phillips-Davies acknowledged the supplier had made a "solid" start to the financial year, but said profits were only "half the story". He added the supplier would monitor its costs and pass on savings if possible, pointing out that it had reduced its gas prices by 4.1% in the spring.
"We have cut prices this year to reflect the fall in wholesale gas costs and we constantly review these," he said.
"We are expecting to see a fall in energy supply profits over the full financial year due to our cut and existing price guarantee.
"We continue to keep a close eye on all costs and if we can cut prices again we will."