The Health Secretary warned Britain "faces a tipping point" and ministers will have to take more measures if the public does not follow Covid-19 regulations.
Mr Hancock told Sky News’ Sophy Ridge on Sunday programme he was “very worried” about the second wave of the virus now emerging in the UK.
“We have a choice," he said. "Either everybody follows the rules – the rule of six and the need to self-isolate if you have a positive test or if you are contacted by NHS Test and Trace – or we will have to take more measures.
“I don’t want to see more measures, more restrictive measures, but if people don’t follow the rules that is how the virus spreads.”
His comments came as the Government announced people in England will face fines of up to £10,000 if they refuse an order to self-isolate.
Mr Hancock said: “We will support people who do the right thing and we will come down hard on people who do the wrong thing.”
He added that there was a danger the infection rate could “shoot through the roof” if people did not follow the the Government’s rules.
“We have seen in the data that some people who need to self-isolate are not doing so,” said the Health Secretary.
“If you have been asked to self-isolate then you either definitely have the coronavirus or you are highly likely to have coronavirus, and so it is mission critical that you isolate.
“I am very worried about this second wave. We have seen in other countries around Europe how it can absolutely shoot through the roof.”