He said the emergence of the new variant meant the JCVI was now also reassessing its recommendations on whether under-18s should be jabbed.
The committee has decided that 16 and 17-year-olds should now have a second jab and Mr Whitty said it is now looking closely at whether that should be extended down to 12-year-olds.
Asked about whether children under 12 should start to be vaccinated, Prof Whitty said: “The evidence, as it has come in, has made us more reassured about safety rather than less reassured.
“I think that most parents would agree that there are now significant outbreaks among those who are not vaccinated in schools, indeed amongst some of those who are vaccinated.”
Prof Whitty also urged people to “raise a glass” to Covid scientists this Christmas.
He said: “If I can make one Christmas plea, it would be that when people raise their glasses this Christmas, they do so to the extraordinary scientists who produce the vaccines, the diagnostics, the drugs, which will allow this Christmas, if possible, to be in a very different place to what it would have been without them.”
Sir Patrick Vallance, the Chief Scientific Adviser, said a key “defence” against omicron was to increase people’s overall immunity to Covid via the vaccine.
Almost 17 million people have had a third booster jab since they started to be rolled out in September.
Last Monday, 7.1 million people aged 40-49 in England became eligible for a third shot via the NHS booking service.
The Telegraph understands ministers are now keen for the booster to be rolled out to everyone over 18 and for the waiting time between the second and third shot to be cut from six to five months.
The move comes as scientists are trying to work out how effective the vaccine will be against the new omicron variant that was first identified in South Africa last week.