Chief executive Jonathan Brearley said: “We can’t predict everything, and the wholesale market, as we’ve seen, has gone up and down extremely quickly so we can’t predict fully what that will be.
“But, looking at the costs that are in the system, we are expecting a significant rise in April.”
However, he said the regulator will not change the cap from its current levels until then.
He added: “This is a really concerning time for customers … We understand how difficult it is.
“The price cap is there to protect customers against unfair profits, but legitimate costs do have to be passed through.”
Bills are expected to rocket this winter for consumers whose fixed-term contracts are coming to an end.
And in April next year, the price cap, which applies to around 14 million households across the UK, will rise again.
Experts at Cornwall Insight expect the price cap to increase from the current level of £1,277 per year, already a record, for an average household, to £1,559 per year.
The latest warning from Ofgem comes as Business Secretary Kwasi Kwarteng meets leaders from industries that use a lot of energy to speak about the rising costs of gas, amid separate warnings of a steep rise in bills for consumers.
The minister will discuss the ongoing spikes in costs with the Energy Intensive Users Group (EIUG), which represents industrial sectors with the heaviest energy consumption in the UK.
UK gas prices have increased dramatically since the start of the year, and reached an all-time record earlier this week.
It has put pressure on businesses which rely on burning gas to run their manufacturing plants – as the gas price goes up, so too do their costs.
EIUG includes UK Steel, the Chemical Industries Association, the Confederation of Paper Industries, the Mineral Products Association, the British Glass Manufacturers’ Federation, the British Ceramic Confederation, industrial gas company BOC, Air Products and the Major Energy Users Council.
The meeting is due to take place on Friday afternoon, with Mr Kwarteng expected to find out whether any industries are slowing production and what support is needed to avoid closures.
On Thursday, the minister said that by getting more renewables on to the grid, the Government could protect households against major energy spikes from volatile fossil fuel prices.