With cases rising across the country, Mr Hancock said there was a danger the numbers could “shoot through the roof” unless effective action was taken to halt the spread of the virus.
His warning came as the Government announced anyone in England who refuses an order to self-isolate could face a fine of up to £10,000.
The Health Secretary said that hospital admissions for the disease were doubling “every eight days” and would be followed by an increase in the number of deaths.
“This country faces a tipping point,” he told BBC1’s The Andrew Marr Show.
“If everybody follows the rules – and we will be increasingly stringent on the people who are not following the rules – then we can avoid further national lockdowns.
“But we of course have to be prepared to take action if that’s what’s necessary.”
During a round of broadcast interviews, Mr Hancock said the Government had taken the decision to impose a legal duty on people to self-isolate if instructed as the data showed some were failing to do so.
At the same time ministers have said people on benefits in England will be eligible for a one off support payment of £500 if they face a loss of earnings as a result of being required to self-isolate.
Mr Hancock told Sky News’ Sophy Ridge On Sunday programme: “We will support people who do the right thing and we will come down hard on people who do the wrong thing.”
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