Video report by ITV News Political Correspondent Paul Brand
The stricter lockdown measures, announced via Mr Hancock’s Twitter feed at around 9pm and later posted online, mean members of different households are not be able to meet indoors.
Labour leader Sir Keir Starmer described announcing such a major decision on social media alone was a "new low for the Government’s communications".
Sir Keir suggested the announcement would have been better suited to a press conference.
The restrictions, which came into force at midnight on Friday, cover the whole of Greater Manchester, as well as the east Lancashire boroughs of Blackburn with Darwen, Burnley, Pendle, Rossendale and Hyndburn.
Residents in the West Yorkshire areas of Bradford, Calderdale – which includes the town of Halifax – and Kirklees – which includes the town of Huddersfield – are also affected.
Sir Keir tweeted: "No one would argue with putting in place local action to reduce the transmission of coronavirus.
"But announcing measures affecting potentially millions of people late at night on Twitter is a new low for the Government’s communications during this crisis.
"When the government ended the daily press conferences, they said they would hold them for ‘significant announcements’, including local lockdowns. It’s hard to imagine what could be more significant than this."
Scottish National party MP Dr Philippa Whitford said: "Do you seriously think this is the way to announce such a huge #Lockdown – 10 o’clock at night to start at midnight?
"What about all those who aren’t on Twitter? Maybe if you hadn’t stopped #COVID19 daily updates – but then again, you’d have to try to talk sense!"
Representatives of the affected areas also took issue with the timing and manner of the announcement.
Shadow business minister Lucy Powell described the way in which the Government had announced the new coronavirus restrictions on parts of northern England as a “disaster”.
Speaking on Times Radio, the MP for Manchester Central said: “I mean announcing them two hours before they come into effect is a bit of a bolt out of the blue.
“With no one around to be able to answer some of the basic questions, I really think is not the way to build confidence and to take people with you and maximise compliance with these steps.”
She said she has been “inundated” with questions which she did not know the answers to from her constituents about the new lockdown restrictions.But Mr Hancock insisted the new rules are “crystal clear”.
The Health Secretary told Sky News: “Well of course, you know it is absolutely crystal clear, precisely as you said, what the new rules are.
“And we brought them in to target specifically the problems that we’ve been able to see through the data because we want to keep the control of the spread of this virus, we want to do that with the minimum impact on people’s lives.
“I appreciate these decisions do have significant impacts on people’s lives but we want to do it with the minimum impact.”
Leeds North West MP Alex Sobel said: "Government gave information very late and with a lack of clarity to local councils, MPs and it seems within the Department of Health.
"The lack of planning and clarity of what to do in different scenarios is breathtaking. Surely they planned these scenarios out!"
Before the announcement was made, Leicester Mayor Sir Peter Soulsby said that he did not have "a clue what’s going on".
He said: "I don’t even know who’s taking the decision and they certainly don’t involve anybody who knows anything about our city."
Despite the confusion in the lead up to the announcement, some supported the government decision to take action.
Mayor of Greater Manchester Andy Burnham backed the government's move, saying it was right to take action in the north of England after it became clear that the picture on Covid-19 cases had changed.
He told Sky News: "On the substance, we do accept that these steps are needed. They’re modest steps.
"We’re asking people not to have visitors at home, if they go to the pub to stick within their own household – steps that hopefully will prevent much more severe restrictions if we take firm action at this time.
"And the reason for it is the picture changed in Greater Manchester over the last week. We’re watching the data very, very closely, like the government is.
"So when the government contacted me to say, ‘look we think something is happening here’, I could already see that it was and it wasn’t just in one locality, there was a change across all of our boroughs and that’s why we said to the government they were right to take quick action."
First Minister of Scotland Nicola Sturgeon also backed the government’s decision, tweeting: "The UK Government is right to act quickly if they think the situation warrants it.
"But this is a sharp reminder that the threat of this virus is still very real. Please abide by all #FACTS advice and stay safe."