Save the Children and the Wellcome Trust are among those calling on Boris Johnson to begin donating vaccines through Covax.
This scheme aims to provide jabs for low and middle-income countries.
The government said it will share “the majority of any future surplus” vaccines “when these are available”.
The UK, which has ordered 400 million vaccine doses and will have many left over, has said it will donate most of its surplus vaccine supply to poorer countries.
The lower income countries most likely to receive the first vaccines through Covax include Afghanistan, Haiti, DR Congo, Ethiopia and Somalia.
So far, more than 29 million UK adults have received a first dose of a Covid vaccine.
In a letter, the charities say the UK is “one of the world’s highest per-capita buyers” of vaccines and is on track to have more than 100 million surplus doses.
“There is therefore the high risk that the UK will be hoarding limited supply whilst health workers and the most vulnerable in low and middle-income countries do not have access,” the letter says.
“The UK will be sitting on enough surplus vaccine doses to vaccinate the world’s frontline health workers twice over.”
The group urges the UK to immediately begin donating doses through the Covax initiative.
Sage scientist Sir Jeremy Farrar, director of the Wellcome Trust, said the UK will still have contractual access to at least 100 million surplus doses once the entire population is vaccinated, which he said “won’t be of use in the UK”.
“Now is the time to think beyond our borders,” he said. “The world won’t be safe while any single country is still fighting the virus.
“If left to spread, it risks mutating to an extent where our vaccines and treatments no longer work. This goes beyond ethics – it’s a scientific and economic imperative.”
Charities that signed the letter include anti-poverty campaigns One and Global Citizen, the Results UK charity and the Pandemic Action Network.
The government said the UK has “played a leading role in championing global access to coronavirus vaccines”, including a £548m contribution to the Covax Advance Market Commitment.
This makes the UK “one of the largest donors” and the contribution “has already helped 20 lower-middle countries to receive doses”.
“The prime minister has confirmed the UK will share the majority of any future surplus coronavirus vaccines from our supply with the Covax pool, when these are available,” a spokesman said.
“No-one is safe until we are all safe.”