However, it could be early June before the 62,000 households in the borough who are not on the direct debit system receive the cash.
Chancellor Rishi Sunak announced the Council Tax Energy Rebate scheme in February as a one-off payment to help people shoulder the burden of cost of living rises caused by huge hikes in energy bills.
The £150 payment will be automatically paid into the bank account of households in band A-D properties that pay council tax by direct debit.
A total of 160,909 households in Kirklees are eligible for the money, which does not need to be repaid.
Local authorities such as Kirklees Council are responsible for making the payment – and for working out how to pay. That includes members of the public who do not pay their council tax by direct debit.
They will need to apply individually for the rebate via an energy rebate application form, which the council aims to make live “soon after” May 23.
Coun Paul Davies (Lab, Holme Valley South), the council’s cabinet member for corporate, said the authority began processing payments to Kirklees residents who pay their council tax by direct debit last week, with the first payments reaching people’s bank accounts on May 6.
He added: “We are currently processing 10,000 payments, which equates to £1.5m, every working day. The order of these payments is randomised.
"This will continue over the next few weeks, with all direct debit payers having received their rebate by May 23.
“Once the online application process opens to those who don’t pay their council tax by direct debit, which will be soon after May 23, we aim to process all payments swiftly and get money in people’s bank accounts within two weeks of a successful application.”
Among those who have sought clarity on the speed and targeting of payments is senior Liberal Democrat councillor John Lawson (Cleckheaton), who has described the rebate as “a sticking plaster” for anticipated energy price rises in the autumn.
He said: “I welcome any help that can be given to people who are struggling with the cost of living crisis and I’m glad that these payments are now underway.
“I think the size of the administrative task shouldn’t be ignored and the question should be asked: how much did it cost Kirklees taxpayers to deliver Mr Sunak’s clumsy benevolence?”