Boris Johnson is expected to agree to the delay of lockdown easing in England and, according to a new poll, just over half of the UK public is backing the move.
The lifting of the last remaining coronavirus restrictions had been planned for 21 June under the government's road map.
But, due to concerns about the rapidly-spreading delta variant, this is likely to be postponed - possibly until the middle of July.
Dr Raghib Ali, a government adviser on COVID-19, told Trevor Phillips On Sunday that a delay to lifting lockdown is "inevitable", and he "expects" the prime minister to say that "a delay is needed to make sure that we don't get to the situation again where the NHS is unable to provide care to all its patients".
He added: "Hospitals are extremely busy at the moment, the emergency departments last month were the busiest they have been for years because of the huge backlog of patients that didn't come in during the previous waves.
"Even a relatively small increase in hospital admissions from COVID will have a significant impact on all our non-COVID patients.
"We really can't afford for those people to suffer any more; they have already suffered enough over the last 18 months."
An Opinium poll of 2,002 UK adults found that 54% thought the lifting of restrictions should be postponed, up from 43% two weeks ago.
Just 37% thought they should go ahead as planned or earlier, down from 44% two weeks ago.
Most of those wanting to postpone the easing are older adults, including almost two-thirds of over-65s, while young people are more evenly split - 45% of those aged 18 to 34 back postponement and 46% say the easing should go ahead on 21 June or earlier.
Around six in 10 people backed keeping the requirement to wear face masks, as well as keeping nightclubs closed and limiting large outdoor events.
Just under half backed keeping restrictions on weddings and the rule of six in people's homes.
Professor Andrew Hayward, a member of the Nervtag group, says that the UK is facing a "substantial" third wave of infection, telling the BBC's Andrew Marr: "I think if we were to open up more that would really fan the flames and lead to this increasing even faster."
Meanwhile, Stephen Reicher, a member of the Scientific Pandemic Insights Group on Behaviours (Spi-B), says that the delay is a "bump in the road", telling Times Radio that "there will be a finish line" and that "vaccinations are going to make a difference."
"Not a complete difference, nothing is perfect in this world, but, yes, we will get there," he added.
One of the main reasons for keeping the restrictions would be so that more people can get their second dose of a COVID-19 vaccine.
The second dose raises the protection provided by the Pfizer vaccine to 88% and the AZ vaccine to at least 60%.
Scientists estimate that 96% of all new cases of coronavirus are attributed to the delta variant, which is estimated to be 60% more transmissible than the previously dominant alpha (Kent) variant.
There have been 42,323 cases of the Delta variant confirmed in the UK, up by 29,892 from the previous week, according to Public Health England.
Mr Johnson said on Saturday that the rise of the variant was a matter of "serious, serious concern".
He is expected to agree to put the final easing of controls on hold for up to four weeks when he returns to Downing Street later from the G7 summit.
The prime minister is likely to face opposition from some MPs and business groups who will see a move to keep the current restrictions as a bitter blow.
Earlier in the week, their were concerns that a delay could slow the country's economic recovery, while one unnamed minister told The Sunday Telegraph that there was a "very short window" in which to open up, otherwise controls might have to remain until spring next year.
"I am very worried the people who want to keep us shut down now want us to keep us shut down permanently and are aiming for 'zero COVID'," the minister was quoted as saying.
"Once you start delaying to the spring you're making this type of control of people's lives semi-permanent."