Covid-19's grip on the nation was amplified on Sunday when it was confirmed a further 54,990 people have tested positive for the virus, in addition to 454 fatalities.
It was the sixth day in a row in which more than 50,000 people tested positive for the respiratory disease.
“We don’t rule anything out, and we’ve shown repeatedly that we will look at the public health advice and we will take the public health advice in terms of what is needed to control the spread of the disease," Mr Hancock told Sky News.
“This new variant is much easier to catch, it is much more transmissible, and we’re now seeing the effect of that in lots of different parts of the country, unfortunately.
“And it means that whereas the old Tier 3 was able to contain the old variant, that is proving increasingly difficult in all parts of the country.”
Asked whether Tier 4 restrictions work, Mr Hancock said: “It is down to people’s behaviour, frankly.
"What matters is, yes of course, the rules that we put in place, but it is also about how people act.
“And frankly what I would say is this: it is critical that everybody in the country does all that they can to reduce the spread of the virus.”
Mr Hancock was echoing what Boris Johnson said on Sunday, when the prime minister signalled tougher tier restrictions could be put in place.
"What we are doing now is using the tiering system, which is a very tough system... and, alas, probably about to get tougher to keep things under control," Mr Johnson told the Andrew Marr Show.
"But, we will review it."
On a more positive note, the first doses of the Oxford University and AstraZeneca vaccinate were administered on Monday.
Dialysis patient Brian Pinker, 82, was the first person to receive the jab and said it "means everything" to him. The NHS would be able to deliver two million doses of the coronavirus vaccine per week if it receives enough supplies, the Health Secretary has said.
Mr Hancock told BBC Breakfast: “If the NHS needs to go faster, then it will go faster. If there were two million doses a week being delivered, then the NHS would deliver at that speed.
“That’s the critical question, but that supply isn’t there yet, and we are working very closely with the manufacturers.”