The total number of cases involving the variant in England so far is 13.
The confirmed cases have been identified in Liverpool, London, Norfolk, and Nottingham.
The University of Nottingham confirmed that one of its students had been found to have the omicron variant, adding that the student “has been off campus and self-isolating throughout the period of infection.”
The spokesperson also said: “We are supporting them in liaison with the public health authorities and wish them a speedy recovery.
“This underlines the importance of everyone following the new government restrictions introduced today.”
In Scotland, there are nine confirmed omicron cases – five in Lanarkshire and four in the Greater Glasgow and Clyde health board area.
Across the UK, there are now 22 cases caused by the omicron variant that is feared to be more contagious than the delta variant.
Officials said individuals who have tested positive and their contacts are all isolating.
Work is under way to identify any links to travel to southern Africa, where the variant was first detected, the UKHSA said.
Dr Jenny Harries, chief executive of UKHSA, said: “It is very likely that we will find more cases over the coming days as we are seeing in other countries globally and as we increase case detection through focused contact tracing.
“That’s why it’s critical that anyone with Covid-19 symptoms isolates and gets a PCR test immediately.”
All nine cases in Scotland are linked to a single private event on the 20 November and all have been self-isolating, First Minister Nicola Sturgeon has said.
At a press conference, PM Boris Johnson said his plan was for all adults to have been offered a booster jab by the end of January.
He said that new vaccination centres will be “popping up like Christmas trees” in order to get as many people vaccinated as possible to “stop the rapid seeding” of the variant.
Mr Johnson said that his government would be deploying “at least 400 military personnel” to help the NHS and volunteers.
He added: “We’ve already done almost 18 million boosters across the UK but we’ve got millions more to do to protect the most vulnerable.
“Then we’ll move down the cohorts rapidly, and working together with the devolved administrations we want to ramp up capacity across the whole United Kingdom to the levels we achieved in the previous vaccination effort.
“We’re going to be throwing everything at it in order to ensure that everyone eligible is offered that booster, as I say, in just over two months.”
The PM said that he is “pleased” to be getting his booster jab on Thursday, adding: “I’ve been waiting patiently for my moment to come ... So whenever your turn comes, get your booster and ask your friends and your family to do the same.
“It’s time for another great British vaccination effort. We’ve done it before and we’re going to do it again. Let’s not give this virus a second chance.”
Health secretary Sajid Javid, who was also at the press briefing, said that the NHS Covid booster jab programme would be put “on steroids” to meet the government’s target.
He added: “If we want to give ourselves the best chance of a Christmas with our loved ones, the best thing we can all do is step up, roll up our sleeves, and get protected when the time comes.”
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