In Ashfield, 95 per cent of households will qualify for the rebate, while in the Nottingham Unitary Authority district, which includes Bulwell, 84.7 per cent qualify.
But that still leaves 3,920 homes in Ashfield and 24,931 in Nottingham UA that will not.
And the Institute for Public Policy Research (IPPR) think tank believes there will be low-income households among those missing out, simply because council is tax is based on the value of someone’s home rather than their income.
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Some 5.2 million households in England will not qualify for the rebate designed to help people through the energy crisis.
These households will be left fighting over a £144 million pot of cash being handed out via local councils - equivalent to just £28 each.
And because the council tax rebates are targeted at lower- and mid-value homes, fewer people qualify in areas of the country where house prices are higher.
Chancellor Rishi Sunak announced the scheme on February 3, on the same day that regulator Ofgem revealed average energy bills would rise by nearly £700 per year from April.
But the IPPR called the measure ‘poorly targeted’, saying two million of the poorest people would miss out on the automatic help and would instead have to apply for a handout from the £144 million fund.
It said it feared those on low incomes excluded from the automatic rebates would be ‘reliant on a discretionary scheme for support which could be overwhelmed’.
The £150 discount on council tax will be applied to the bills of qualifying households from April and only households in council tax bands A to D will be eligible for it.
This excludes 4.5 million homes in the higher value bands E to H, some of whom will be on low incomes.
It also leaves out 660,000 households which don’t currently pay council tax, such as student households, analysis of official data by JPIMedia shows.
However, people living in band A to D homes who get local council tax support, where their bills are discounted or written off by the local council, should still qualify.
Second homes and empty homes are ineligible for the payouts.
To help anyone struggling with their bills who doesn’t qualify for the help, Mr Sunak announced a hardship fund of £144 million, to be distributed by local authorities.
He told the Commons this would ‘help those lower-income households who happen to live in higher council tax properties, and households in bands A to D who are exempt from council tax at all’.
The devolved administrations of Scotland, Wales and Northern Ireland are receiving around £715 million funding to deliver help in these nations.
The proportion of households which will miss out on the automatic council tax rebate varies widely across the country.
In London, with its high house prices, a third of homes (32 per cent) will be ineligible for the discount and will have to apply for a payout from the hardship fund if they needed support.
In the north east, where property prices are lower, far more people will get the rebate automatically – only 11 per cent will miss out.
In comparison, in the City of London, the UK’s banking heartland, three-quarters of households (76 per cent) won’t qualify for the automatic help.
England’s council tax system has long faced criticism.
The amount people pay is determined not by their income but by the value of their property more than 30 years ago, in 1991.
Similarly, the Treasury’s decision to base its support on council tax bandings has come under attack.
The IPPR estimates that two million of the poorest people would miss out on the automatic help and would have to apply for discretionary support, while 44 per cent of the richest will benefit from the tax cut.
Henry Parkes, IPPR senior economist said: "Thirty percent of households in London will be excluded from automatic support, by far the highest rate in England, despite the fact London has above average fuel poverty and the highest levels of relative poverty.
“Support should be distributed on the basis of need and incomes through universal credit, not historic house valuations which may not relate to the financial circumstances households actually face, leaving them reliant on a discretionary scheme for support which could be overwhelmed."
Rachel Reeves MP (Lab), the shadow chancellor, told the House of Commons that the scheme ‘will mean that many of the poorest households receive no extra support, while some of the richest do’.
Labour has instead called for an extension to the existing Warm Homes Discount scheme to include more lower-income households.
A spokesperson for the Department for Levelling Up, Housing and Communities said it would be publishing further information on the council tax rebate shortly.