Matt Hancock has said any coronavirus vaccine would not be made compulsory.
The health secretary said there would be such “enormous demand” for vaccinations that making them mandatory would not be necessary.
No vaccine currently exists for COVID-19, with global research ongoing.
Hancock, reminded that he last year said there was a “strong argument” for compulsory vaccinations for children when they start school, said at Monday’s daily coronavirus press conference in Downing Street: “I think the extent of the public’s reaction to following the lockdown shows we will be able to achieve very very high levels of vaccination without taking that step [making it compulsory].
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“While I won’t rule anything out, we are proceeding on the basis that such a huge proportion of the population is going to take this up because of the obvious benefits to individuals, their families, their communities and the whole nation.
“There will be enormous demand for it as and when the science is safe to proceed.”
Hancock was also asked to relay a message to the small pockets of anti-vaccination protesters in the UK and abroad.
The health secretary said: “There has been no greater demonstration in modern history that vaccines save lives than the need for a vaccine to save lives and get the world going again following the outbreak of COVID-19.
“We will only a licence a vaccine when it is effective and safe. If, and when, the independent regulators licence a vaccine in this country, they will do so knowing that it is safe and everybody should follow that advice.”
Meanwhile, Hancock reported 288 more deaths of people who tested positive for coronavirus, the lowest daily rise since 29 March.
He noted the small rise but added that figures tend to be lower after a weekend. This is due to reporting delays. A total of 28,734 people have now died.
It comes with Boris Johnson expected to outline plans to ease the coronavirus lockdown on Sunday.
The prime minister will reveal the government’s strategy to reopen businesses and kickstart the economy following the pandemic, which has seen the country subject to stringent movement restrictions since 23 March.
In a public address on Sunday, the PM will outline plans to ensure the British public feel safe re-entering society when advised it is safe to do so.
These are likely to include a gradual reopening of schools and allowing people to travel to beauty spots for exercise, according to a draft document leaked to the BBC and the Financial Times.