Stoke-on-Trent, Coventry and Slough will move into coronavirus Tier 2 restrictions - and discussions are underway on Warrington, Nottinghamshire and West Yorkshire entering Tier 3.
The Tier 2 changes come into effect from 12:01am on Saturday - meaning people will not be able to meet other households socially indoors.
Mr Hancock said in all three regions, infections have risen to over 100 per 100,000 people, with cases doubling every fortnight.
The expected change for Warrington is "due to a continuing rise in cases there", Mr Hancock said.
"There's an excellent local hospital in Warrington but it is dealing with a very high number of cases," he explained.
And Mr Hancock said "discussions are underway" on whether parts of Nottinghamshire and West Yorkshire will be placed into Tier 3.
This includes the areas in the Midlands controlled by Nottinghamshire County Council and Nottingham City Council.
Nottingham City Council tweeted to say talks are ongoing with the government.
The council said: "Talks are ongoing between council leaders and government about the current COVID-19 situation.
"Leaders continue to stress the need to protect the health and wellbeing of the population as well as local businesses.
"Further updates will be provided as the talks progress."
Mr Hancock also revealed some progress on mass testing.
Lateral flow tests have now started to be rolled out to schools and universities - helpful because they do not require a lab or a machine to deliver the result.
The health secretary said he had purchased "many millions" and they would help "find the virus where it spreads and to reduce the disruption that virus control measures inevitably create".
But Labour suggested some infections and deaths could have been avoided if the government had followed the advice of its scientific experts known as SAGE and instituted a "circuit breaker".
Jon Ashworth, the shadow health secretary, said Prime Minister Boris Johnson should have "taken advantage of next week's half-term" and put temporary national restrictions in place.
"My worry is that the approach the government are currently taking means that there will by necessity need to be tougher, deeper action in the weeks to come," he warned.
"We're only in autumn, winter has not hit us yet."
He also called the latest stats showing Test and Trace had its lowest success rate since the system began "bad".
The three-tier system for England was unveiled by Prime Minister Boris Johnson earlier this month in a bid to simplify the rules, as the country heads into a second spike of coronavirus cases.