Mr Hancock said he hoped the measures, which ban household mixing and encourage people to stay home, could be relaxed.
But he said the data was not yet showing the impact of the rules, which came into effect at the beginning of the month.
Speaking at a Downing Street briefing Mr Hancock said: “It is too early for us to know what the number of cases will be as we come to the end of the current lockdown.
“At the moment, most of the tests we’re getting back, and most of the positive cases, are from around the time the lockdown came in, so we are yet to see in the data – and it’s too early to expect to see in the data – the impact of the second lockdown. But we absolutely hope to be able to replace the national lockdown with a tiered system similar to what we had before.”
Dr Susan Hopkins, a Public Health England director advising the Government’s coronavirus response, added: “We expect if the lockdown is working … that we will start to see cases decline over the next week. We expect it will be longer to see hospital admissions, another week or so, but I think as long as we start seeing cases decline then we can start making a judgment about what are the right decisions that we make and what the opening up decisions that happen on December 2.”
She said Tier 1 coronavirus restrictions had “little effect”, while the impact of Tier 2 varied in different places, as she suggested the tiers may need to be strengthened to “get us through the winter months”.
She told the Downing Street press conference: “We have recognised that the tiering of the country has had a different effect in each area. Tier 3, and especially Tier 3 plus in the North, has had an effect in reducing the numbers of cases in the North West and we can see the North West’s declining number of cases now.
“Tier 2 seems to hold in some areas and not so well in others, and so really it depends on how fast transmission is occurring and how well the individuals in the population are taking that advice in.
“We see very little effect from Tier 1 and I think when we look at what tiers may be there in the future we will have to think about strengthening them in order to get us through the winter months until the vaccine is available for everyone.”
It comes after Welsh Health Minister Vaughan Gething said people should not expect a “definitive statement” on Christmas in the next few days or weeks.
Mr Hancock said one of the main goals now was to use the mass rapid testing roll-out to find those who are asymptomatic with the virus to avoid further restrictions.
And he said the UK had secured five million doses of a promising jab to protect against coronavirus after the “brilliant news” that the new vaccine could be more than 94 per cent effective.
Mr Hancock announced that the UK had struck a deal with US firm Moderna for a batch of its vaccine, which British scientists have hailed after trails showed it may be 94.5 per cent effective against the illness.
Interim data suggests the jab is highly effective in preventing people getting ill and may work across all age groups, including the elderly.
The UK has already secured 40m doses of a vaccine from Pfizer/BioNTech, which uses the same technology as Moderna and should be in the UK before Christmas.
And Mr Hancock said a further deal had been struck for the new vaccine, but it would not arrive until Spring next year at the earliest.
He said: “Across diagnostics and vaccines, great advances in medical science are coming to the rescue. While there is much uncertainty, we can see the candle of hope and we must do all that we can to nurture its flame. But we’re not there yet. Until the science can make us safe we must remain vigilant and keep following the rules that we know can keep this virus under control.”
Earlier Downing Street would not rule out making vaccination mandatory although officials stressed there were “no plans” to make a coronavirus jab compulsory.
While Mr Hancock defended ordering just five million doses of the Moderna vaccine, enough for 2.5m people.
He said: “I pay tribute to the Vaccine Taskforce who have done this buying, concluding the Moderna deal today.”
Business Secretary Alok Sharma had worked “incredibly hard on getting this over the line, including today”, Mr Hancock added.
But he stressed that the Moderna vaccine would not be available until spring and the UK had orders for others which could be in use earlier.