The combined hikes would mean capped energy bills would have more than doubled in less than 12 months, reaching almost £2,800 for customers at default rates, the body said.
Rishi Sunak used his spring declaration last month to provide aid of £300 per household to help meet an expected rise in energy bills later this year, but resisted cuts in green levies.
He previously announced support for households, including a £150 council tax refund and a £200 refundable energy bill rebate.
But he was criticized by other Tory MPs who felt the measures did not go far enough to ease the pressures households face with rising bills and inflation.
A Downing Street source said nothing was ruled out, adding that the abolition of green energy taxes would not happen until the autumn when it would be “one of many options”.
“We’re a long way from fall and we’re not ruling anything out,” the source said. “Some of our MPs really like it, we understand it’s an interesting option that some are pushing.”
They added that at the time of the spring statement, it was decided that the levy should remain in place, but that could change by the fall.
“We were balancing many goals, including the climate goal,” the Downing Street source said. “We didn’t feel it was the right thing to do in March. But we cannot exclude that the situation will be different later in the year.