Ex-Prime Minister Tony Blair is urging the government to give as many people as possible an initial dose of a Covid vaccine - rather than preserving stocks so there is enough for second jabs.
The Pfizer-Biontech and Oxford University-Astrazeneca vaccines require two doses to be fully effective.
Mr Blair said his idea would speed up the vaccine programme so the country could come out of lockdown sooner.
In the Independent, he argued the roll-out must be "radically accelerated".
The UK has pre-ordered 40 million doses of the Pfizer-BioNTech vaccine and 100 million of the Oxford University Astrazeneca vaccines.
More than 500,000 people in the UK have now been given their first dose of the vaccine.
The two doses of the Pfizer-BioNTech vaccine are administered around 21 days apart.
In a statement, Pfizer said this was needed "to provide the maximum protection", adding: "Health professionals are advised to continue to follow the official guidance on administration of the vaccine."
Mr Blair told BBC Radio 4's Today programme that although "you really need the two doses… the first dose gives you substantial immunity".
He argued there was a "strong case for not holding back the second doses of the vaccine" and instead using those batches to give a greater number of people the first dose.
His proposal was backed up by Professor David Salisbury, the man in charge of immunisation at the Department of Health until 2013.
He told Today the numbers were "straightforward".
"You give one dose you get 91% [protection] you give two doses and you get 95% - you are only gaining 4% for giving the second dose," he said.
"With current circumstances, I would strongly urge you to use as many first doses as you possibly can for risk groups and only after you have done all of that come back with second doses."
However, he acknowledged this would be harder to do with the Oxford University vaccine, where the efficacy of two doses is 60%.
Pfizer has not tested their vaccine as a single dose so where have the numbers come from?
The large clinical trial using two jabs showed 52% protection in the time between the first and second jabs.
But it takes time for the immune system to fully respond, so that figure will include the time when there is no protection from the vaccine.
And this is true of the second jab; it's not an instantaneous response.
Data in the New England Journal of Medicine says there is 90.5% protection in the six days after the second jab.
Prof Salisbury's argument is this is all down to the first jab, as the second has not kicked in yet.
Professor Wendy Barclay, from the department of infectious disease at Imperial College London, said Mr Blair's idea was interesting but agreed it was "too risky" to try without further evidence.
And Professor Neil Ferguson, also from Imperial, added that the UK regulator had authorised the vaccine on the basis that people would receive two doses.
Administering one dose only would require "an entirely different regulatory submission", he told a Commons committee.
A Department of Health and Social Care spokesperson said: "Over the coming weeks and months, the rate of vaccinations will increase as more doses become available and the programme continues to expand."
Mr Blair's suggestion is part of a seven-point plan he has drawn up, which also includes a plea to the government to start preparing "health passports".
The former Labour prime minister, who was in power between 1997 and 2007, predicted that in six months, countries would only allow travellers to visit if they could give proof of their disease status.
He also said it was important to "have the best data systems in the world available to us".
"Collecting this data in one place, with one patient record, is going to be absolutely vital - testing, vaccinations, every single thing to do with the development of this disease," he added.
"You need to record every single piece of data you can lay your hands on because we will be adjusting our vaccination programme as we go - we may even have to adjust the vaccine itself."
Mr Blair also said that while it was important to prioritise the vulnerable and health care staff, this should not delay vaccinating those who were more likely to spread the disease, such as students.
Tony Blair's theory about making vaccines go further is grabbing the headlines but the former prime minister's thoughts on health passports could prove even more controversial.
He's confident that within six months no country in the world will allow travellers in without proof of their disease status - and wants the UK government to get ahead of the curve, building a vast database of patient records, tests and vaccinations.
It would seem inevitable that any health passport would end up being used not just for foreign travel but at home, with restaurants, shops and even employers demanding to know about an individual's virus status.
The national ID card that Tony Blair's government proposed in the teeth of fierce opposition would finally become a reality.
But civil liberties and data rights campaigners have already raised concerns about issues such as the data collected by the NHS Covid-19 contact tracing app, and about the role in building a virus dashboard the government has given to the controversial American firm Palantir.
They can be expected to mount a vigorous fight against any attempt to create a national "Covid passport" - and many MPs across the political spectrum will share their unease.
But not everyone will reject the idea out of hand. Some whose freedoms to leave their house or to welcome family at Christmas have been curtailed may think that giving away some of their data is a price worth paying for a return to normality.