The new legal duty requires people to self-isolate if they test positive for coronavirus, or are traced as a close contact.
And Mr Hancock said he was "very worried" about the latest data suggesting Britain could be on the same path as Spain and France - where deaths and hospitalisations are increasing - without effective action. "We've seen in Europe it can shoot through the roof".
"It comes back to this central point that the balance between the measures we take nationally and the measures we take locally, according to local rates of infection, is a critical balance to get right".
"We were all promised this fantastic track and trace system, the testing was going to be incredible".
Repeating this view later on the BBC's Andrew Marr show he added: 'I'm not in this for a popularity contest.
With infections on the rise, the United Kingdom test and trace system is under strain and millions of people across the country have been placed under local restrictions.
Hancock revealed that discussions are underway today regarding a possible closure in London.
This graph shows how Kent's infection rate is much lower than the national average
London Mayor Sadiq Khan is now pressing ministers to extend the controls to the capital, which he believes may be just "two or three days" behind the hotspots of the North West and North East of England.
Professor Whitty and Sir Patrick are expected to say at 11am this morning that Britain is "heading in the wrong direction" as No10 warned Brits they are in the "last chance saloon" to avoid a second national lockdown or very strict restrictions.
Another lockdown would deliver a further blow to an economy that shrank more than any other major developed country during the pandemic.
The opposition Labour Party leader Keir Starmer said he would support whatever measures the government brings forward, but criticised the government's testing system for not having the capacity to deal with increased demand as schools returned.
He said: "The testing capacity we have is valuable".
Britain's government said Sunday it is introducing fines up to 10,000 United Kingdom pounds, or $13,000, for people who refuse an order to self-isolate, which will go into effect on September 28.
The government will help those on lower incomes who face a loss of earnings as a result of self-isolating with a one-time support payment of 500 United Kingdom pounds ($633).
This story has been published from a wire agency feed without modifications to the text.