Residents struggling to make ends meet will get an extra £30 off their council tax – meaning thousands will see up to £180 wiped from their bill this year.
Local politicians agreed to give the one-off reduction to 30,200 low-income households that already pay less council tax.
The scheme will cost £906,400 and comes out of a £1.9m cash handout from the government to help people cope with the cost of living crisis.
People in council tax bands A to D are already getting a £150 government rebate to help with soaring energy costs.
Town Hall number-crunchers said some people will miss out on this extra help, so they have decided to give the extra discretionary money to them.
They include 3,195 families in council tax bands E to H who are on a low income – they will get £150 from the discretionary fund.
People who move into their homes in the next year will get between £75 and £150 depending on when they move in.
The council is also expecting 2,000 residents who do not pay council tax but are still liable for energy bills to apply for a £150 grant to pay for heating and lighting.
Residents who get a council tax reduction or housing benefit will get the payment automatically.
Others will have to apply online, via a dedicated phone line, or in a face-to-face appointment.
The council has to spend the extra government cash by November so people will not be able to apply for funds after that.
The scheme was agreed at the last cabinet meeting before May’s council elections.
Further hardship funds are expected from the government.