The new variant of coronavirus now accounts for a third of cases in London, the education secretary said.
With two doses of a vaccine “not enough” Mr Zahawi encouraged people to get a booster jab – those aged 30 and over are eligible to do so from Monday.
As of Sunday, there have been 3,137 confirmed cases of the Omicron variant in the UK.
But the true number is likely to be far higher.
There were 48,854 new positive Covid cases reported across the UK on Sunday – there have been 360,480 cases in the last seven days.
Scientists from the London School of Hygiene and Tropical Medicine (LSHTM) have warned that the UK will face a substantial wave of Omicron infections without further restrictions beyond the Plan B measures announced last week.
These include recommending people work from home if they can, expanding mask-wearing rules and introducing Covid passes for entry to some venues – parliament will vote on the changes on Tuesday.
People in England with two or more jabs who are close contacts of Covid cases will be told to take daily lateral flow tests for seven days from Tuesday.
It means people in close contact with suspected or confirmed Omicron variant cases no longer need to self-isolate.
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Mr Zahawi told One’s Andrew Marr Show the new variant was a “big bump in the road” on the journey from pandemic to epidemic.
He said a “national endeavour” was needed on the vaccine roll-out with the country in a “race against Omicron”.
The current measures in response to the variant were “proportionate”, the education secretary added.
Asked by Andrew Marr if he could guarantee all schools would be open in January, Mr Zahawi said he would do “everything in my power” to ensure all of them stayed open and protected but he stopped short of giving a guarantee.
He also said there was no plan at the moment to vaccinate primary school-age children against Covid.