Sheffield Council has received £3m to make the coldest homes in the city more energy efficient and warmer.
The Government funding will improve 500 council, 15 housing association and 265 private homes, particularly Victorian properties.
It can only be spent on homes with a household income of less than £30,000 a year and work has to be completed by December.
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Officers say because of the tight timescale, funding will be given on a first come, first served basis but Green councillors were unhappy.
Coun Douglas Johnson said: “As soon as you have any sort of grant application process on a first come, first serve basis, it is the capital rich people in big houses who can get in the door far more quickly than the Bangladeshi couple in Darnall.
“I want to make sure we don’t have the council doing good work encouraging people to apply but they’re still not ahead of those in the six bedroom house with an application in on day one.”
Green councillor Paul Turpin agreed. “You’ve got the semi-retired couple in a six bedroom house in Broomhill and then you’ve got the single dad of four in Gleadless who’s working on a building site on minimum wage.
“They’re both equally eligible yet clearly the couple, who may have been former professionals, are going to be more equipped to apply for the grants and can apply on day one because they’ve got the time and the wherewithal. They will then be ahead of the person that you could argue is in greater need.”
Labour has the majority on the Executive and said the grants should remain first come, first served.
Deputy Council Leader Julie Grocutt said: “I know it seems quite harsh and rigid but we know we will get a lot of applications and we need to be as transparent as possible in the way that we deal with them. If we add an element of officer discretion, that opens us up to challenges.”