The Department of Health and Social Care (DHSC) on Friday told people in Pendle and Blackburn in Lancashire, as well as Oldham in Greater Manchester, not to socialise with anyone outside their household from midnight on Saturday.
Public transport should only be used if it is essential and the number of people attending weddings, civil partnerships and funerals should be limited to no more than 20, made up of household members and close family only, the department said.
The Government said a rise in people testing positive for coronavirus in Blackburn, Pendle and Oldham was due to “social mixing”, particularly among 20 to 39-year-olds.
But leaders in the region have complained the restrictions have been imposed without “detailed guidance” and have caused confusion.
The Labour leader of Pendle Council Mohammed Iqbal told the BBC’s Today programme on Saturday the restrictions, which the council argued against, had been “imposed” to “punish people who have been testing flat out”.
He added: “The Government has announced these tightening restrictions for local people in my area, yet they have not issued any detailed guidance as to how it will operate, who will police it.
“So local people are actually more confused than they were on Thursday evening.”
Oldham Council leader Sean Fielding told BBC Breakfast that there were a number of things that needed clarified because the announcement of the restrictions had not been “the smoothest”.
He added: “There’s a number of different points we are going to have to provide clarity over as we move forward because the announcement itself from the Government wasn’t the smoothest.
“It was leaked to a local newspaper at lunchtime so before it was actually official the news was kind of out there.
“So there was clarity to be sought at that time and I’m afraid to say there’s still some clarity around particular aspects of the restrictions that we are seeking to find and put out ourselves.”
Greater Manchester Police also took to social media on Saturday to tell people not to call 999 or 101 for clarification about Covid-19 measures.
It tweeted: “Please do not call 101 or 999 for clarification on COVID-19 regulations.”
The tighter restrictions were announced by the DHSC as holidaymakers scrambled to get home to beat new quarantine measures.
From 4am on Saturday travellers arriving to the UK from Croatia have to self-isolate for 14 days after a spike in coronavirus cases led to the Government removing Croatia from its safe travel list.
Friday’s announcement on new Covid-19 restrictions in the North West stopped short of a localised lockdown, where businesses would be closed.
The Government said people can still shop and go to work and that schools and other childcare settings will open as normal under the new restrictions.
Mr Fielding said that a full lockdown was avoided by a pledge to provide more enforcement capacity to take action against people breaking the rules.
He added: “Part of our discussions with Government which helped us to avert the kind of economic lockdown of the kind in Leicester was a pledge around increasing the capacity in our enforcement teams so that we could take action where we had reports of businesses or premises or households not following the rules.
“So when we receive those reports we now have additional capacity around enforcement and compliance to take action, whether it’s fines, whether it’s closure orders or whatever.”
Mr Fielding also said that that the local authority was enlisting the help of celebrities to get the new coronavirus restriction messages across.
He added: “We’ve enlisted support of the Pakistani cricket captain (Azhar Ali) who has recorded a video for us to get the message out to communities that might listen to him rather than listen to me.
“We have used the actor that played Jay in the Inbetweeners (James Buckley) for example, so we have been really creative in using assets within our communities and also celebrities or whatever it might be that might be more effective in telling people the restrictions and why it’s so important that they follow them.”
Also on Friday it was announced that Birmingham is being added to a watch list as an “area of enhanced support” and Northampton becomes an “area of intervention”.
Meanwhile the Greencore sandwich factory in Northampton was closed from Friday, with staff and members of their households having to isolate for 14 days.
It was announced last week that more than 200 people had tested positive for Covid-19 after an outbreak linked to the factory.
The Department of Health said Health Secretary Matt Hancock will bring in regulations “to ensure that this self-isolation period is legally enforced” and warned that anyone who does not abide by the rules without a reasonable excuse could be fined.
Restrictions in Wigan, Rossendale and Darwen have been lifted, the department said, bringing them into line with the rest of England.
Figures published on Friday show there were 71.7 new cases per 100,000 people in Oldham in the seven days to August 18, down from 112.2 over the previous seven days.
Pendle, which is in second place behind Oldham, has a rate of 67.3, down from 108.6, while Blackburn with Darwen is in third place.
There, the rate has fallen from 88.2 to 56.1.