Speaking at Tuesday's cabinet meeting, Chris Ward said he hoped the remaining 12,000 would all have received their money within the next eight weeks.
He said 'almost everybody' who pays their council tax bill by direct debit had been sent the money and the final letters inviting those who pay by other means to claim their sum had recently been sent out.
'We were writing letters at a rate of 4,000 a week to those that aren't on direct debit and those have now all been done,' he said. 'We're now waiting on responses to come back in and processing them as soon as they do.'
He said £150 credit would be applied to council tax bills of any households that do not claim.
The rebate was introduced by the government this year to mitigate the cost of rising energy bills.