The Local Government Association said cuts of £3.3 billion in central government funding next year would be followed by further falls in the following two years.
The cuts will leave English authorities facing an estimated funding gap of of £9.5 billion by the end of the decade, the Association claimed.
Leeds City Council leader Judith Blake said: “We know there are further significant cuts to council finances on the way, but vulnerable people in our communities are already suffering and especially in northern cities which have taken a much bigger hit than the south east, which cannot be right or fair and is a situation that needs addressing with firm action rather than just words.”
She added: “As a city Leeds has lost more than 40 per cent of its core funding since 2010 while the figure for the wider Leeds City Region is a combined £470m less in that time, so we have already taken a lot more than our fair share and continuing with even deeper cuts to come is simply not sustainable and is potentially dangerous.”
Local Government Minister Marcus Jones said: “These unsubstantiated and premature claims are based on funding decisions which have yet to be made let alone announced.
“Councils have worked hard over the past five years to deliver a better deal for local taxpayers, however, like the rest of the public sector will have to continue playing their part in tackling the deficit to ensure the economic recovery continues.”