People in Oldham in Greater Manchester, as well as Pendle and Blackburn in Lancashire will be told not to socialise with anyone outside their household from midnight on Saturday.
They are also being advised to avoid using public transport unless it is essential.
The number of people attending weddings, civil partnerships and funerals should be no more than 20 people, made up of household members and close family only, the Department of Health and Social Care (DHSC) said.
Friday’s announcement stopped short of a localised lockdown – where businesses would be closed – which Oldham council’s leader Sean Fielding had earlier this week warned could be “catastrophic” for the area.
He tweeted: “We have reached agreement with the Government that Oldham will not go in to full local economic lockdown. Some additional restrictions will be introduced, however.”
The UK 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.
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”.
West Midlands Mayor Andy Street said “some people have not been strict enough” with coronavirus measures and the DHSC said he would be meeting Health Secretary Matt Hancock and local council leaders on Friday to discuss “urgent next steps”.
Meanwhile the Greencore sandwich factory in Northampton is to close 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 UK's Department of Health said Mr 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 Thursday showed there had been 187 new cases recorded in Oldham in the seven days to August 17 – the equivalent of 78.9 per 100,000 people.
This was a decrease from 111.8 in the seven days to August 10.
Pendle’s latest weekly rate was also down to 64.1, while Blackburn with Darwen was 67.5.
DHSC said coronavirus cases are “rising quickly” in Birmingham, with 30.2 cases per 100,000 and more than half of cases in the last week in people aged 18-34.
The new restrictions will not apply in the Darwen area of the Blackburn with Darwen upper tier local authority area, parts of Pendle, in Rossendale or in Wigan.
But they do come on top of the existing ban on indoor gatherings of more than two households in place across parts of Lancashire, Greater Manchester and West Yorkshire.
A spokesman for the Greater Manchester Combined Authority (GMCA) welcomed the fact a local lockdown in Oldham had been avoided and that restrictions in Wigan had been lifted.
He said officials had worked “to ensure areas with consistently low infection rates were taken out of the restrictions, so the decision on Wigan’s restrictions being lifted is a welcome one”.
He added: “We have all been concerned about the situation in Oldham and this is why we have sought to work in partnership both with the local council and the Government to agree the most suitable and effective measures, as set out by Oldham Council.
“Increased measures to restrict the mixing of households are a much more sensible approach than local lockdown. We are pleased that the Health Secretary has listened to what leaders said in their letter to him yesterday.”
Mr Hancock said: “Working with local leaders we agreed further action in Oldham, Pendle and Blackburn. It is vital that everyone in these areas follow the advice of their councils, and abide by their local rules carefully.”
He said they had tried to make the action taken “as targeted as possible, with the maximum possible local consensus”.
