The combined rises would mean price-capped energy bills would have more than doubled in less than 12 months, rising to almost £2,800 for customers on default tariffs, the body said.
Rishi Sunak used his Spring Statement last month to provide £300 worth of support per household to help with an expected energy bills rise later this year, but resisted cutting green levies.
He had previously announced support for households including a £150 council tax rebate and a £200 repayable energy bill discount.
But he came in for a slew of criticism from fellow Tory MPs who felt the measures did not go far enough to ease the pressures households are facing with rising bills and inflation.
A Downing Street source said that nothing has been ruled out, adding that dropping the green energy levies would not happen any earlier than the autumn when it would be “one of several options”.
“We are a long way out from autumn and we wouldn’t rule anything out,” the source said. “Certain of our MPs really like it, we understand it’s an attractive option that some are pushing.”
They added that at the time of the Spring Statement, it was decided that the levy should stay in place, but said this could change by autumn.
“We were balancing lots of objectives, including the climate objective,” the Downing Street source said. “It wasn’t felt that it was the right thing to do in March. But we can’t rule out the situation being different later in the year.”