The energy price cap is predicted to drop below £3,000 as early as April by the boss of Ofgem with possibly even more savings to come in the summer.
Jonathan Brearley said that it was "possible" that falls in the wholesale cost of gas and electricity could mean that bills would fall below that level for the average household.
It is more optimistic than recent projections from independent analysts at Cornwall Insight, who last week forecast the price cap would still top £3,200 in April before falling significantly in July.
If the price cap falls a little below £3,000 for the average household in April it would only save customers a small amount as they were set to pay £3,000 anyway under the Government's price guarantee.
But it could save billions in taxpayer money. The Government has promised to pay suppliers to make up the difference between what they are allowed to charge customers and the price they have to pay to buy energy.
Speaking at an Institute for Government event, Mr Brearley said predictions were still very uncertain, but sounded a rare note of optimism for troubled bill payers.
"On our current projections, although gas prices do remain volatile, the price cap level may fall below the energy price guarantee level in July, and possibly do so as early as April," he said.
"This will save billions of pounds of the expected public spending on that measure.
"Although highly uncertain, it's possible that prices may fall well below this throughout the summer, which would be welcome news for all customers, both households and business."
Mr Brearley also reiterated his support for a new "social tariff", which would mean that less well off households pay less for the energy they use.
"The root cause for some customers, despite the enormous widespread support by Government, is their inability to pay for their basic energy needs," he said.
"Therefore, we think there is a case for examining, with urgency, a social tariff that limits the impact of extremely high prices and reduces volatility for a defined set of vulnerable groups.
"To be clear, this tariff would need to be subsidised when prices are high, and preferably paid for through funds raised in a progressive way."
He said it was down to the Government to decide how to design such a tariff, including deciding who to target it at.
In a wide-ranging speech Mr Brearley said the UK needs to move "as rapidly as possible" away from the international gas market, which has been manipulated by Russia over the last two years.
To help with this, he called for the biggest build-out of new energy infrastructure in more than half a century.
"We will need to build new energy infrastructure at a pace not seen for decades," he said.
"When you look at our history, the period immediately after the Second World War most closely resembles the pace and scale that we need to build.
"From 1950 to 1970, Great Britain's electricity generation capacity expanded around fourfold its original size.
"Since then, the system has been largely stable in terms of our networks."
Mr Brearley added: "To meet the scale of future energy demand between now and 2050, we will need again to build out our infrastructure - onshore, offshore and connecting to other countries - at an extraordinary pace not seen for over half a century.
"This is a huge challenge, but also a huge economic opportunity."
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