Boris Johnson told the House of Commons on Monday that the coronavirus could be conquered thanks to technical developments including testing, drugs and a vaccine. He also claimed the UK could “defeat” the virus “by the spring” of 2021.
It comes after the Prime Minister announced his plans to send England into a second lockdown from Thursday.
But in March Mr Johnson said the nation could “turn the tide” within 12 weeks.
He also previously set out a plan in July for “significant normality” by Christmas.
Mr Johnson also admitted that the new lockdown could possibly be extended beyond December 2.
Speaking about the second lockdown, Mr Hunt said he would rather see the Government tighten its restrictions in order to save lives.
He told BBC’s Newsnight: “I think one thing we have learnt is that scientists don’t always agree and for every decision that the Government announces with a backing of the scientists on Sage there will be another group of scientists that disagree.”
He said it was wrong to “read too much” into what the Government’s Scientific Advisory Group for Emergencies (Sag)e said at the end of September.
Sage called for a short lockdown in England to halt the spread of the virus in September.
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He told parliament: “I believe that these technical developments, taken together, will enable us to defeat this virus by the spring, as humanity has defeated every other infectious disease.
“And I am not alone in this optimism, but I cannot pretend that the way ahead is easy, or without painful choices for us all.”
The UK’s vaccine chief suggested that a vaccine, if approved, may not go to half of Britons.
Current plans in the UK involve prioritising 10 groups for a vaccine which includes over-50s, NHS staff and the vulnerable.
During his interview on Newsnight, Mr Hunt said he has always advocating for acting earlier in tackling the virus.
He added: “It might be less painful later but I think now what’s clear underneath the kind of political noise in the House of Commons there is a pretty strong consensus that we need to do this.
“What really matters now is whether we use the lockdown wisely and we have got some long standing issues in the way that our test and trace system has been working which now is the chance to really sort out.”
All non-essential shops as well as pubs, restaurants, hairdressers and more businesses will close during the second lockdown.
Mr Johnson said it “made sense” to focus initially on local restrictions.
Labour leader Sir Keir Starmer accused Mr Johnson of a “catastrophic failure of leadership”.