Londoners have so far received only a tenth of the vaccines administered across England, despite being home to 16 per cent of the population.
A total of 447,329 doses have been administered in the Midlands, the first to vaccinate a patient as part of the programme, with 387,647 people receiving at least one injection.
But London has delivered just 237,524 doses and the capital's mayor Sadiq Khan said he was "hugely concerned".
The NHS England figures indicate about half of people aged 80 and over in north-east England and Yorkshire have received their first dose.
By contrast just three in 10 people aged 80 and over in eastern England have had their first jab, with a similar proportion in London.
Downing Street defended the operation, with the Prime Minister's official spokesman telling reporters: "We've rolled out the vaccination programme across the country and we've ensured that every area receives a fair share of the vaccinations and we will continue to do that.
"You will continue to see the vaccination programme accelerate through this month and throughout February and the PM's been clear that we will ensure there is a vaccine centre close to everybody by the end of the month."
The North East and Yorkshire was just behind the Midlands in terms of doses administered, with 433,045, according to the NHS England figures which run up to January 10.
The data, the first time a regional breakdown has been given, shows 2,371,407 jabs were given between December 8 and January 10, including first and second doses.
There were 318,445 vaccinations in the North West, 411,257 in the South East, 285,332 in the South West and 236,023 in the East of England.
There were 2,452 listed as other, including some people who live in Scotland and Wales.
Mr Khan said: "I am hugely concerned that Londoners have received only a 10th of the vaccines that have been given across the country.
"The situation in London is critical with rates of the virus extremely high, which is why it's so important that vulnerable Londoners are given access to the vaccine as soon as possible."
He later said he had had a "constructive" meeting with vaccines minister Nadhim Zahawi.
A spokesman for the NHS in London said: "We have more than 100 vaccination sites up and running across London, including the NHS Covid-19 vaccination centre in the ExCeL London, and more are opening all the time.
"London is getting its fair share of vaccine supply for the priority groups we have to vaccinate by mid-February."
Boris Johnson has previously acknowledged that while parts of the country were doing "incredibly well" in vaccinating people it was "less good" in other areas.
Up to January 10, 1,036,605 people aged 80 or over had received a first dose, as had 960,699 under-80s.
Separate figures from NHS England show nearly a quarter (23%) of first doses in England up to January 7 went to people aged 49 and under.
Just over half (53%) went to people aged 80 and over.
Some 12% went to people aged 50-59, 6% to those aged 60-69, and 6% to those aged 70-79.
The priority groups for vaccination include all staff working in care homes and frontline health and social care workers.
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