Levelling Up Secretary Michael Gove. Photograph: Parliament UK

Labour representatives in London have accused the government’s new levelling-up white paper of leaving the poorest Londoners “out in the cold”.

Levelling Up Secretary Michael Gove unveiled the flagship policy document on Wednesday after revealing the 12 “levelling-up missions” that aim to spread prosperity “to all parts” of the country.

But of the £4.7 billion allocated under various levelling-up funds so far, analysis has shown that some of the poorest areas of the country – many of which are in London – are receiving less money than some wealthier areas.

Hackney, which is one of the most deprived local authorities in England according to the government’s indices of multiple deprivation, is set to receive just £0.16 of funding per head, while Barking and Dagenham is to receive just £3.93 per head.

By comparison, wealthier areas are set to receive far greater levels of support, such as Bromsgrove in Worcestershire, which will have access to £148.33 per head.

Labour’s London Assembly economy spokesperson Marina Ahmad said the allocation of funds “doesn’t make sense” and will “do little to address the real poverty in our communities”.

She said: “After many long years of austerity, it is incredibly important that ministers undo the huge damage it has caused by properly investing in the poorest areas in our country.

“What ministers fail to realise is that many of these are in London. Downgrading the capital’s economic recovery runs against any levelling-up agenda.

“Disappointingly, this strategy will leave Londoners out in the cold and do little to address the real poverty that exists in our communities.”

Mayor of London Sadiq Khan, who has struck a more cordial tone with ministers as he seeks a new funding deal for Transport for London, welcomed the publication of the white paper and said he wants to work with the government to “help level-up London and every other town, city and region in the UK”.

But he warned that “levelling up the UK must not be about levelling down London”.

Khan said: “When London succeeds our whole country benefits – and vice-versa. That is why I want to work with the government, other regions and business, to help level-up London and every other town, city and region in the UK.

“However, if the government is to succeed with its mission, it must recognise that levelling up the UK must not be about levelling down London and withholding the funding and investment our capital city desperately needs.

“London has some of the most deprived communities in the country and they deserve support and funding just as much as other parts of the UK.”

Speaking on Sky News on Wednesday morning, Michael Gove said: “The Chancellor gave us a huge cheque in the spending review and now we are spending it. We’re making sure in Wolverhampton, in Sheffield and in other areas that we put our money where our mouth is, and that we make sure that money which, in the past, was spent too much in London and the South East, is now spent in the North and the Midlands where it’s needed.”