The Government said that urban councils in England would lose PS80 per household but Sigoma says that when funding reserved for community and public health services is removed, the cut is as big as PS162.
Official figures suggest that Yorkshire and Humberside councils had lost 2.6% of their funding for core services, but latest figures calculated by Sigoma show a reduction of 7.3%.
A Sigoma spokesman said councils looking after some of the poorest communities faced the biggest reduction in their spending power.
Sir Steve Houghton CBE, chairman of Sigoma and leader of Barnsley Council, said "The Government continues to penalise councils trying to serve some of the most vulnerable people in the country.
But according to SIGOMA, the Special Interest Group of Municipal Authorities, the true figure is 7.1 per cent, because the the Government includes ring-fenced budgets and reserved funds, such as public health money which cannot be cut or moved to plug gaps in other services.
SIGOMA chairman and leader of Barnsley Council Sir Steve Houghton CBE said "The Government continues to penalise councils trying to serve some of the most vulnerable people in the country.
Councillor Stephen Houghton, leader of Barnsley Council and chairman of SIGOMA
, said: 'We are arguing for a fairer deal for all in the new local government funding formula.
has warned that 2015 is expected to be the year where councils are likely to have to make the toughest decisions about cutting frontline services and councils will face an uphill battle to support their most vulnerable people.
Local government think tank SIGOMA said the figures show some of the country's poorest boroughs are subsiding the richest.
Stephen Houghton, chair of the SIGOMA group, which is open to unitary authorities outside London, called for a change in the "social services anomaly".
Local Government think-tank SIGOMA
, made up of local authorities, said the figures show some of the country's poorest boroughs are subsiding the richest.