Unicef UK estimated that Britain could give away 20% of its projected available stock and still meet its target to give all adults their first dose of vaccine by the end of July.
The charity warned that the success of the vaccination programme in the UK could be “reversed” if supply is not shared.
Concerns have been raised that while the virus rages in other parts of the world there is more chance for new variants to emerge.
And experts have suggested that new variants could potentially escape the protection afforded by the vaccines.
Unicef UK called on the Government and other G7 countries to start sharing vaccines through the vaccine sharing facility Covax from June to ensure that vulnerable people in countries around the world can be vaccinated.
This would help prevent further spread of variants as well as open up society for children, it said.
Unicef UK director of advocacy, Joanna Rea, said: “The UK has done a fantastic job in rolling out Covid-19 vaccines to more than half of its adult population and we should all be proud of what has been achieved.
“However, we can’t ignore that the UK and other G7 countries have purchased over a third of the world’s vaccine supply, despite making up only 13% of the global population – and we risk leaving low-income countries behind.
“Unless the UK urgently starts sharing its available doses to ensure others around the world are protected from the virus, the UK will not be safe from Covid-19.
“Our vaccine rollout success could be reversed and the NHS could be fighting another wave of the virus due to deadly mutations.”
On Monday Professor Chris Whitty, chief medical officer for England, said the way to prevent or minimise the number of new variants is to “get on top of” the pandemic globally.
And the World Health Organisation said there was a “shocking disparity” in access to Covid-19 vaccines between rich and poor countries.
WHO director general Dr Tedros Adhanom Ghebreyesus told a press briefing: “The shocking global disparity in access to Covid-19 vaccines remains one of the biggest risks to ending the pandemic.
“High and upper-middle income countries represent 53% of the world’s population, but have received 83% of the world’s vaccines.
“By contrast, low and lower-middle income countries account for 47% of the world’s population, but have received just 17% of the world’s vaccines.”
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He added: “How quickly we end the Covid-19 pandemic and how many sisters and brothers we lose along on the way, depends on how quickly and how fairly we vaccinate a significant proportion of the population and how consistently we all follow proven public health measures.”
A UK Government spokesperson said: “The UK has played a leading role in championing global access to coronavirus vaccines.
“We are one of the largest donors to Covax, providing £548 million to deliver more than a billion vaccines to lower-middle income countries this year.
“So far, this funding has already helped deliver vaccines to more than 70 countries, including 38 across Africa.
“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.”