The exact eligibility criteria for the discretionary funding is being set by each council, meaning the support varies from place to place.
People will need to get in contact with their local authority, or check their website, to see if they qualify for support.
For example Camden Council in London has opened up its discretionary scheme to those living in bands A to D who “have received one payment but are still struggling”.
Households who receive Council Tax Support or “with no recourse to public funds” will be prioritised, the council said.