Millions of Covid vaccines could be wasted if rich countries send large amounts of leftover doses to poorer nations in one go, Unicef has warned.
The charity said there needed to be a steady supply throughout the year because poor countries do not have resources to use them all at once.
The UK and others have promised to donate their surplus doses - but they have been asked to give more earlier.
Stars including Billie Eilish and David Beckham are backing Unicef's plea.
The celebrities have signed a letter to the G7 group of rich countries - including the UK - asking them to donate 20% of their vaccines by August.
"The pandemic will not be over anywhere until it is over everywhere," said Beckham.
The other stars who have signed the letter include Andy Murray, Olivia Colman, Ewan McGregor, Liam Payne, Priyanka Chopra Jonas, Orlando Bloom, Katy Perry, Gemma Chan, Whoopi Goldberg, Claudia Schiffer and Chris Hoy.
Unicef's vaccine lead Lily Caprani told BBC Newsnight that countries needed to vaccinate their own populations at the same time as the rest of the world.
"At some point, no doubt, we will need to vaccinate under-18s," she said. "But the priority at this moment has to be making sure that all of the vulnerable and priority groups around the world get vaccines.
"So we're saying countries like the UK and the G7 need to donate their doses to those low income countries now, while still vaccinating their populations at home."
But last week, Health Secretary Matt Hancock said vaccinating children in the UK would take priority over sending doses abroad.
Unlike other countries, the UK has not revealed how many doses it plans to donate to the Covax vaccine-sharing scheme, saying only that it will donate its excess doses. On Friday Mr Hancock said the UK did not currently have any spare doses.
Earlier this week more than 100 former prime ministers, presidents and foreign ministers urged leaders of the G7 countries to pay two-thirds of the £46.6bn needed to vaccinate low-income countries against Covid.
Ex-PM Tony Blair said the "reality" was that governments are "obliged to look after [their] own people" and so will always prioritise vaccinating their own country first.
But he said, "you can't be absolutist about this, there may be some vaccine that we can ship out in advance".
Another former UK PM, Gordon Brown, said the G7 and other wealthy nations "should pay their share" to help parts of Africa and Asia.
He said it should not be left to a "whip round" to deal with a "disease that has got to be brought under control."
Unicef's Ms Caprani called on G7 countries to start donating jabs now as well as throughout the summer and the rest of the year.
"Low income countries need a steady supply that they can get off the tarmac and into the arms of health care workers," she said.
"The unintended consequence of saving all these vaccines up to Christmas time is that countries won't be able to absorb them and roll them out and therefore they could end up going to waste. We could see millions of doses of vaccines not used and expiring, and that will be a tragedy."
In their letter, the celebrities said Unicef was already delivering vaccines in poor countries - but the charity was 190 million doses short.
The letter said the G7 countries - the UK, Canada, France, Germany, Italy, Japan and the US - will soon have enough to donate 20% of their doses between June and August without significant delay to their own rollouts, and doing that would provide more than 150 million doses to Covax.
"The virus is still spreading in many countries and producing new variants with the potential to put us all back where we started," said the letter to the G7 group.
Some of the celebrities such as tennis star Murray are also urging people in the UK to donate to Unicef's VaccinAid appeal.
Some countries, like the UK which has ordered 400 million doses of various vaccines, have already vaccinated a large proportion of their citizens.
But other countries are still waiting for their first shipments to arrive. Many poorer countries are relying on deliveries from Covax.
At the G7 summit later this week, Prime Minister Boris Johnson is planning to urge setting a target to vaccinate the world by the end of 2022.
Campaigners and critics - as well as a group of MPs - say action needs to be taken now and Britain should donate a dose for every jab imported into the UK.
The UK government has already donated £548m in aid money to the Covax scheme, and half a billion doses of the Oxford/AstraZeneca jab have been ordered by other countries and sent abroad.
The leaders of the seven G7 countries are meeting in Cornwall for their annual summit this weekend.
The US, France, Germany, Italy and Japan have all said how many doses they will donate to Covax. Like the UK, Canada is yet to put a figure on their planned contribution.