The UK's vaccine advisory body is expected to announce later whether it will approve an expansion of the Covid vaccine booster programme.
A third case of the Omicron variant , and Number 10 has already set out measures to contain it.
Prof Anthony Harnden, JCVI's deputy chairman, said it would be a "sensible strategy" to reduce time between doses and extend boosters to more age groups.
Regulations on face masks and isolation rules are due before Parliament today.
An urgent meeting of health ministers from the G7 group of nations will be held today "to discuss the developments on Omicron", the Department for Health said.
Early evidence suggests the new Omicron variant - initially reported to the World Health Organization from South Africa on Wednesday - has a higher reinfection risk.
The first UK cases - picked up from analysis of recent positive Covid tests from all around the country were confirmed on Saturday in Essex and Nottingham.
The third case identified on Sunday came from a visitor who spent time in the Westminster area of London, although the person is no longer in the UK, the Health Security Agency said.
The agency said it was "very likely" more cases would be found in the coming days.
Because there are also high levels of cases of the dominant Delta variant, Health Secretary Sajid Javid said at the weekend he would be asking the JCVI to consider backing the rollout of booster jabs to a wider population than at present.
Prof Harnden, from the Joint Committee on Vaccination and Immunisation, told USAGovNews Radio 4's Broadcasting House programme on Sunday that there was a "strong argument" for extending boosters to all adults.
"Accelerating the booster programme both by extending the age range and by reducing the interval between the second dose and the booster dose would be a sensible strategy," he said.
The committee only advises the government and the final decision on measures to combat Covid always lies with the politicians - but Prime Minister Boris Johnson has said he intends to wait for the recommendations from the scientific experts who make up the committee.
Currently, booster jabs have been restricted to those aged 40 and over, front-line health or social workers, and those with health issues.
Asked in the Radio 4 interview whether everyone over 18 should expect an invitation to get a booster jab, Prof Harnden responded that the offer would come "earlier than we have previously envisaged".
The government announced at the weekend that face coverings will become compulsory in shops and on public transport in England, and pupils in Year 7 and above, plus school staff and visitors, are being advised to wear face coverings in communal areas.
UK arrivals will have to take a PCR test from Tuesday and self-isolate until they receive a negative result.
Prime Minister Boris Johnson at a Downing Street news conference on Saturday, adding that they would be reviewed in three weeks.
Under the rules due to come in on Tuesday:
The government agreed last year to give MPs a vote before introducing new pandemic measures.
This means the latest measures, due to be laid before Parliament later today, need a majority in the Commons before they will go ahead.
Historically the PM has faced opposition to coronavirus restrictions from among his own backbenchers.
Conservative MP Steve Baker, deputy chairman of the Covid Recovery Group, told the Daily Telegraph the measures "will cause chaos" in schools as, under the rules, children will likely be forced into self isolation.
"The government needs to explain when all of this will be brought to an end," Mr Baker said.
Meanwhile, in a virtual address to the SNP conference, Scottish First Minister Nicola Sturgeon will urge people to "pull together" over the winter months to stop spread of the Omicron variant.
By doing so, she is due to say, there is a greater chance of a more normal Christmas.