Lockdown restrictions in Leicester can be lifted - but not all
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In a statement, he told the Commons virus rates in the city "still remain well above the national average and the average for surrounding areas".
He added: "We're now in a position to relax some but not all of the restrictions that were in place.
"From July 24 we'll be removing the restrictions on schools and early years childcare and taking a more targeted approach to the restrictions on non-essential retail."
Mr Hancock said: "The latest data shows that the seven-day infection rate in Leicester is now 119 cases per 100,000 people and the percentage of people testing positive is now at 4.8%.
"These are positive indicators, especially in light of the huge increase in testing."
He compared the figures to when the lockdown was imposed and the seven-day infection rate was 135 and 10% of tests were positive.
He added: "I committed to reviewing the measures in Leicester every two weeks. This morning I chaired a gold meeting of the local action committee to discuss the latest situation and this afternoon I held a further meeting with local leaders, Public Health England, the JBC, the local resilience forum and my clinical advisers."
Mr Hancock said: "Restrictions like those for travel and only having social gatherings of up to six people, for example, will remain in force.
"And measures introduced on July 4 like reopening the hospitality sector will also not yet apply."
Mr Hancock paid tribute to the people of Leicester and Leicestershire for their "perseverance and hard work".
He told the Commons: "Some say that the local lockdown is unnecessary. I wish this were true, but sadly it remains vital for the health of everyone in Leicester and the rest of the country that these restrictions stay in place.
"We will review them again in a fortnight. I hope that this careful easing of restrictions will provide some comfort to people in Leicester and Leicestershire.
"And I'd say this directly to people of Leicester and of Leicestershire: I pay tribute to you all. Your perseverance and your hard work has brought real and tangible results and you've shown respect for one another."
Mr Hancock told MPs of an issue relating to testing: "We've identified some test swabs that are not up to the usual high standard that we expect and we'll be carrying out further testing of this batch.
"As a precautionary measure, and while we investigate further, we're requesting the use of these Randox swab test kits are paused in all settings until further notice.
"This problem was brought to my attention yesterday afternoon, we contacted settings using these swabs last night and published the pause notice immediately.
"Clinical advice is that there's no evidence of any harm, the test results are not affected, there is no evidence of any issues with our other test swabs and there is no impact on access to testing."
Shadow health secretary Jon Ashworth began his questions by asking about comments from the Government's chief scientific adviser, Sir Patrick Vallance, in relation to Sage advice to lock down the country in March.
He said: "Why did it take a further seven days for the Government to implement lockdown if Sage was advising March 16?"