The announcement came ahead of the next national tier review which will take place on 30 December, with any announcements expected the day after. Herefordshire had only been moved down to Tier 1 on Saturday.
The Isles of Scilly will remain in tier one and will be the only area in England to have that status.
Areas that have been placed in tier three are Bristol, Gloucestershire, Somerset, Swindon, Isle of Wight, New Forest, Northamptonshire, Cheshire and Warrington.
He said there had been "sharp rises" in cases and hospital admissions.
- Why are these changes being made now?
Mr Hancock said Covid-19 is spreading at a "dangerous rate" across large parts of England and it is "better to act sooner".
John Edmunds, a professor who is a member of the Scientific Advisory Group for Emergencies, which advises the United Kingdom government on its coronavirus response, also said further measures would be necessary because the new variant of the virus was already spreading across the country.
The UK government has expanded the new Tier Four restrictions, with more parts of England now subject to stricter rules.
There are also "some early signs" of the new variant and rising cases in the South West which also now faces tougher restrictions.
The new mutant strain of coronavirus has led to a turbulent week - and a somewhat dampened festive season - in the UK.
It comes as cases in Norfolk continue to increase, with the new variant thought to be responsible for more than a third of the county's cases.
- What is being done to try and contain this new strain?
Anyone who has been in South Africa in the past fortnight and anyone who is a close contact of someone who has been in South Africa in the last fortnight must quarantine immediately.
Asked if he could guarantee there would be no new restrictions for December 25, he added: "There is absolutely no plan to do so".
In more positive news, the Health Secretary announced that vaccinations were now being rolled out into care homes, with the Chelsea Pensioners receiving the jab.
Mr Watt said if there were any cases of coronavirus the islands would be "extremely vulnerable".
And those who work in care homes, he assured, will be tested for the disease twice a week.
Under tier two rules people can not spend time indoors with others outside of their household or bubble.
The number of people living in Tier 2 will fall to seven million, or 13% of the population of England.
The move from Tier 1 - medium alert - means that people in Cornwall can no longer follow the rule of six outdoors and cannot mix with other households indoors unless they are in a support bubble.
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