On Tuesday, the Lancashire authority’s director of public health Dominic Harrison announced the new measures to be followed for the next month with the aim of avoiding a local lockdown.
The restrictions include a limit of two people from the same household allowed to visit another home.
Figures published on Tuesday showed Blackburn had 47 cases per 100,000 people in the seven days to July 11, up from 31.6 cases per 100,000 in the seven days to July 4.
The authority is third on the list of highest weekly rates, behind Leicester, which has a rate of 118.2 cases per 100,000 and is subject to a local lockdown, and nearby Pendle, with a rate of 76.6.
Mr Harrison said, if rates were continuing to rise in a few weeks, the council would consider reimposing some lockdown restrictions.
Residents are being told to wear cloth face coverings in all enclosed public spaces, including workplaces, libraries, museums, health centres and hair and beauty salons.
Mr Harrison also called for people only to bump elbows with anyone outside of their immediate family, instead of shaking hands or hugging, and said public protection advice for small shops was being stepped up to ensure measures including social distancing and increased ventilation were being followed.
Targeted testing is taking place in the borough, with a mobile testing unit at Witton Park Academy as well as a facility at Royal Blackburn Hospital, and residents have been told they do not need to have symptoms to be tested.
Mr Harrison said: “These steps will help and we are appealing to everyone in Blackburn with Darwen to follow them to protect themselves and their loved ones.
“If we don’t, a local lockdown, like in Leicester, becomes a very real possibility.
“The council is working with the NHS and the wider community on this, it’s up to us all to help each other stick to the advice that’s been given.
“We can only avoid further lockdown measures if we work together.
“In the next week to 10 days, we will see a rise in the number of cases in the borough due to the increased targeted testing we are doing in communities most at risk, and because we have opened a Pillar 2 testing site next to the hospital last week.
“In another two weeks, if the rates are continuing to rise, we will have to consider reversing some of the national lockdown lifting measures locally one by one until we see a reversal in the current rising trend.
“It’s up to everyone to make sure we don’t have to do that.”
Seventy new cases of coronavirus were recorded in the local authority in the seven days to July 11, up from 47 in the previous seven days.
Council leader Mohammed Khan said: “I can reassure all local residents that the council is working with different agencies and organisations across the borough to help get the message out to everyone that life cannot go back to normal just yet, and we must all make sacrifices to avoid a local lockdown.
“We are doing everything we can to get a grip on the virus, and we need everyone in Blackburn with Darwen to pull together to help us.
“Please continue to do your bit to stick to the rules to protect yourself and your family.”
In Pendle, people were also warned to stay alert after the authority reported an increase in cases, particularly in Nelson and Brierfield.
Director of public health for Lancashire Dr Sakthi Karunanithi said there were signs of ongoing household transmission and reminded people to stay at home if they had symptoms, wash their hands regularly and avoid or limit large family gatherings inside.
He said: “With the slight increase in the Covid-19 infection rate in Pendle, it’s really important to stay alert to the risks.
“We should all do what we can to limit the spread of infection.
“”It can feel like things are back to normal, but we are still in the middle of a pandemic and there is risk for the virus to come back.”