Vauxhall MP Florence Eshalomi said she has been told London has only around 5,000 doses left of the jab, while experts told the Standard current supply could be depleted in as soon as ten days.
A smallpox vaccine is currently mostly being offered to men who have sex with men who are considered to be at highest risk of exposure from monkeypox.
The latest data shows that of the UK’s 2,883 confirmed or likely cases, 2,047 were recorded in London, mainly among gay, bisexual or other men who have sex with men.
Ms Eshalomi told the Standard the Government had been “asleep at the wheel” and called for “urgent action” to get on top of the outbreak.
“Haven't we learnt anything from Covid and AIDS,” she asked.
“In the latest figures reported by the UKHSA, Lambeth tops the league for the number of cases and we know that monkeypox cases are now spreading into every region of the country while the vaccination campaign against the virus is faltering.
“I have been told that London only has 5000 doses left centrally.
“If we are to get ahead of the curve, we need more vaccines. One thing the government should be doing is obtaining a licence from the manufacturer of the vaccine to allow us to make the vaccine in this country.”
The British Association of Sexual Health and HIV told the Standard that current estimates suggest only 8,300 vaccines remain available, with around 5,000 earmarked for London.
This means it is “likely that the remaining number of vaccines will run out in approximately 10 to 20 days, leaving a gap in supply until the next shipment arrives in September”.
It said the roll-out was “slow” and being hampered by “lack of centralised leadership” - and that the Government needed to order as many as 250,000 doses.
Health officials say 150,000 doses were ordered - 50,000 of which have already been distributed to the NHS and a further 100,000 set to come on-stream next month.
Ian Green, CEO of leading sexual health charity the Terrence Higgins Trust, said the shortfall needed to be taken “seriously at the highest level of government”.
“There needs to be urgent action to salvage this situation,” he said.
“We know many gay and bisexual men will be worried by news of vaccine supplies running low and our advice to them is please do not panic”.
Mr Green called on transparency from health officials on supply, and for remaining stocks to be prioritised for those at risk in places with high cases like London, Brighton, Manchester and Essex.
A UK Health Security Agency spokesperson was unable to confirm numbers of doses left available for London.
Demand for the UK’s current supplies of smallpox vaccine is high among those eligible. Extensive queues formed outside previous walk-in clinics that were offered at Guy’s Hospital in central London.
These have since been made by appointment only.
The UKHSA’s Dr Mary Ramsay said: “The roll out is continuing at pace, with the vaccine being offered to individuals at higher risk of coming into contact with monkeypox in order to offer them protection and to help contain the current outbreak.
“The remaining approximately 100,000 doses is expected to arrive in the UK in September.
“The thousands of vaccines administered by the NHS to date among those at highest risk of exposure should have a significant impact on the transmission of the virus.”