Mr Sunak told allies the UK was approaching a “fat lady sings” moment when lockdown must be lifted.
An ally of the Chancellor said: “This needs to be the last time we do this. This is the fat lady sings moment. We can’t lock down again.
“Rishi is concerned that the scientists have been moving the goalposts in recent weeks.
“It’s no longer just about hospitalisations and protecting the NHS but cases and case numbers."
The source added that the “talk has switched to becoming Covid-free” following the emergence of worrying, highly transmissible variants of the virus discovered in Kent and South Africa.
Experts fear that high circulation of the virus makes mutations more likely - which could reduce the efficacy of vaccines.
Britain’s immunisation campaign has surged ahead of many countries in Europe and the West, with over 10 million Brits having received the jab as of yesterday.
A study released earlier this week also suggests that the jab developed by Oxford University and Astrazeneca cut transmission by up to 66 per cent in another boost in the fight against the bug.
But Professor Chris Whitty last night warned that while the UK was “past the peak” of deaths and hospitalisations, the NHS would continue to be under pressure until all over-50s had been inoculated.
The CMO told a Downing Street briefing that the number of people in hospital is still higher than in the first peak in April last year - and deaths would "stay high for quite some time".
His comments were echoed by Boris Johnson who said that the level of infection is still "forbiddingly high" and that it is too soon to relax current restrictions.
It comes as experts warned that social distancing measures could remain in place until Spring next year despite the success of the vaccination programme.
Paul Hunter, professor in medicine at the University of East Anglia (UEA), warned against “getting too excited” about the findings of the Oxford study.
He told The Sun: “Yes it will reduce transmission.
“But we showed a couple of weeks ago in a preprint that even if every single person in the UK was vaccinated with the Oxford vaccine it would not bring the R down to less than 1.”
The Prime Minister has said before exiting the lockdown is even considered, the R rate needs to have clearly come down, along with hospitalisations and deaths.
Prof Hunter said with an R over 1, “the infection would still spread, although we would see substantially less severe disease.
“I suspect we will have continue to have some degree of social distancing till at least spring 2022.”