The Floods Recovery Minister John Healey is reported to be working with authorities, including Hull City Council and East Riding of Yorkshire Council on a funding package.
According to the Hull Daily Mail's website, Hull is expected to receive more than£400,000 to help people displaced by the floods, while£100,000 will go to the East Riding.
In Gloucestershire local newspaper websites say Tewkesbury BC, Gloucester city Council, Forest of Dean DC and Cotswold DC will receive more than£1m.
It has been estimated that, at the end of July, more than 1,400 families in the area were still unable to return to their homes.
Mr Healey is quoted: "For those worst hit it will take more time. I don't want them paying council tax for homes they can't live in.
“That's why I reminded councils they have the discretion to grant discounts to residents still out of their homes.
“And in a special step in recognition of these special circumstances I promised Government funding so that other local taxpayers don't have to cover the cost.
“We are working with 22 councils on funding worth more than£1m, which means 2,300 families will not pay council tax on homes they can't live in.”
LGCplus reported last month that, across the country, those still out of their homes numbered 3,400 and that 62 local authorities hit by last year floods are to receive£13m because of the damage.
The authorities - including badly hit areas such as Gloucestershire, Tewkesbury and Swindon - will get cash from the government's 'restoration fund' to rebuild their communities.