The forecaster, which is widely regarded for its accurate predictions, said a household using a typical amount of gas and electricity would pay £1,823 a year.
The figures emerged as Energy Secretary Ed Miliband wrote an urgent letter to Ofgem, the regulator which sets the price cap, asking it to move quickly to protect consumers.
The predicted higher prices will take effect at the same time as increases to water and council tax bills in April.
However, minimum wage levels will also go up while benefits and the state pension will increase.
Cornwall forecasts that the price cap will rise from its current level of £1,738 per year for a typical household.
Higher household bills are likely to add pressure to the government who are already facing criticism for removing the winter fuel allowance from elderly people not claiming the pension credit or other means-tested financial support.
Ofgem will announce the official new energy price cap level on 25 February, which will affect homes in England, Wales and Scotland.
The predicted rise will come as the days get lighter and warmer, when energy use tends to fall.
Cornwall say the hike is due to a combination of colder weather and a fall in gas storage levels across Europe, which has led to a sharp rise in wholesale prices.
Bills are about 50% higher than pre-Covid levels, but remain below the peak reached in 2022 when Russia’s full-scale invasion of Ukraine caused energy prices to spike.