Thousands of letters about how to claim the energy rebate scheme were sent to the correct addresses in Liverpool but with the wrong name.
The energy bills rebate was announced earlier this year to help households with rising energy bills.
Last week, Liverpool City Council sent 10,000 letters to households across the city inviting them to apply for the scheme.
These were households who do not pay by direct debit and use other methods, such as standing orders.
However, an error led to these letters being dispatched having wrong names on them.
The council has confirmed that there is no possibility a person can claim the energy rebate inappropriately using the details contained in the letter as it “undertakes identity and bank account checks before it makes a payment”.
The local authority added: “We will now investigate this matter in accordance with our data breach protocols.
“We are very sorry that this has happened and the correct letters will start to be sent to affected households from Friday. It will include advice to destroy the original letter and a reminder on how to apply for the energy rebate online.”
Last week, it was reported that a primary school in Liverpool warned there could be job losses after the local authority’s failure to handle responsibly a major electricity contract.