The lockdown restrictions imposed across the United Kingdom in March will be reinforced in Leicester, the government has announced.
Mr Hancock said the easing of the lockdown planned for the rest of England on July 4 can not happen in Leicester because of rising cases.
Sir Peter said he was glad the health secretary had introduced measures that went beyond just extending the current level of restrictions.
With the city's pubs, bars and restaurants no longer permitted to reopen this weekend, there are fears of people flocking to nearby Derby and Nottingham, for example.
He said: "Given the growing outbreak in Leicester we can not recommend that the easing of the national lockdown set to take place on July 4 happens in Leicester".
In recent weeks, health officials in Leicester have reported an increasing number of infections within the city.
He added that local action has increasingly been taken by the Government in efforts to limit coronavirus infections.
The Health Secretary continued: "We've decided that from tomorrow, non-essential retail will have to close and as children have been particularly impacted by this outbreak, schools will also need to close from Thursday, staying open for vulnerable children and children of critical workers as they did throughout".
"Unfortunately, the clinical advice is that the relaxation of shielding measures due on July 6 can not now take place in Leicester".
"These sorts of much more targeted measures have worked in other outbreaks", Mr Hancock told BBC Breakfast.
A new indoor testing centre will open on Tuesday at the Highfields Community Centre, with further testing sites planned.
The areas include Leicester city centre as well as suburban parts of Leicestershire, including Wigston, Oadby and Blaby.
But he argued: "I've seen what people did during the lockdown across the whole country and people in very, very large numbers, large proportions, followed the rules".
But Mr Hancock appeared to play down suggestions of extensions to the furlough scheme in such areas, saying: "We've also put in money to the local councils so that on a discretionary basis they can use that to support people who need further support."Asked about possible causes for the spike - such as poverty, higher ethnic diversity, language difficulties and higher-density housing - Mr Hancock did not dismiss them. Those shielding were particularly anxious".
Short of building a wall around the city, there is absolutely no way this is going to work.