Council officials say nearly 11,000 eligible Richmondshire households have now received their £150 energy rebate to help ease the pressure of increased energy bills.
Richmondshire District Council says it has paid out more than £1.6 million so far.
The national rebate is available to most households in council tax bands A to D.
Most eligible Richmondshire households that pay council tax by direct debit have already received their rebate.
Letters are being sent out this week to the 3,600 households that do not pay their council tax by direct debit asking them to apply online for the rebate.
Households will need to provide their bank details so that the rebate can be paid to them. When households provide this information, the council is required to carry out checks on the bank details that have been supplied before the payment can be made.
Any household that is eligible but has no bank account, or where the pre-payment bank checks are not matched, or that fails to contact the council to give bank account details will still get their rebate.
In these instances, the £150 will be credited to their council tax account.
Households will need to apply for this rebate by August 31.