Professor Chris Whitty also said COVID-19 cases are "rising again", as the UK recorded its highest ever daily tally on Monday.
Shahzad Ali, CEO at security training company Get Licensed, has warned people not to share pictures of their negative lateral flow tests online.
Government experts in Israel have already recommend a fourth dose of the COVID vaccine for all people over 60 and healthcare workers and similar measures could be implemented in the UK.
The government is aiming to give one million booster jabs each day in the race against the spread of Omicron.
A probable case of Omicron has been identified among the crew of a Norwegian liner that disembarked in New Orleans.
Belgian MEP Pascal Arimont said the attackers were 'cowards' and has reported the incident to police.
New measures in England came into force on Tuesday to try to halt the spread of the Omicron variant.
The prime minister is expected to set out plans for the UK's booster programme later on Tuesday.
Glynn Steel, 54, from Malvern, Worcestershire, died after a two-week battle with coronavirus after refusing the COVID jab because it was tested on animals, his wife said.
Michelle Barlow, 51, died after suffering a blood clot that was 'likely' to have been caused by the AstraZeneca COVID vaccine, an inquest at Bolton Coroner's Court heard.