The organisation, which represents local authorities in the capital, says that the way the premium is calculated is skewed to top up richer areas that receive less funding per pupil.
It claims that schools in Tower Hamlets will receive a pupil premium of just £653 per pupil, while in more affluent Wokingham the figure will be £2,943. It is anticipated that the average premium per pupil will be £2,410.
In a letter to ministers London Councils proposes an alternative method, which it claims better takes into account the level of deprivation funding for each deprived pupil.
Councillor Steve Reed, London Councils’ executive member for children and young people, said: "We assume that it is not the government’s intention to penalise pupils from more deprived areas, but unfortunately that is what its plans look set to do.
"This is not just about London, the most deprived areas around the country will see far less pupil premium funding per child than significantly wealthier areas of the country."
Others to raise concerns about the pupil premium are think tank the Institute of Public Policy Research (IPPR) and charity School Home Support (SHS).
The IPPR is concerned that schools will have too much freedom over how the extra money will be spent. It fears money will be used to meet targets to encourage top performing students to take the proposed English Baccalaureate qualification, rather than used for one-to-one tuition and support for disadvantaged pupils.
The pupil premium is linked to free school meal entitlement, but SHS fears schools could miss out on £230m worth of funding because parents of an estimated 94,000 pupils that are eligible for free school meals are not claiming their entitlement.
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