"If people break the rules, then we are more likely to end up with national measures," Hancock told the BBC broadcaster.
After stressing that "it is absolutely critical that at this moment that everybody stops, takes a step back and realizes we all got a part to do," the health minister said that he does not want to see another national lockdown like the one that was imposed from March to May.
"The public needs to follow the rules, and that's why I say the country faces a choice," he added.
When asked if he would report to the police anyone he sees breaking the self-isolation rules, Hancock said he would, because "the self-isolation part is absolutely necessary … to break the chain of transmission."
Starting from September 28, people will be required to self-isolate if they test positive for COVID-19 or if they have come into contact with an infected person of face the fines, The Guardian said on Saturday.
As of Saturday, 390,358 people had tested positive for the COVID-19 in the United Kingdom, where 41,759 patients have died from the disease since the pandemic began.