The number of local authorities running community testing programmes is expected to reach over 100 with a further roll-out in the new year.
The DHSC said that the participating local authorities had created their own testing plans based on local data and demographics.
It said Oldham will first focus on higher-risk supported living settings, health and social care staff, schools, and colleges.
Lancashire will prioritise large manufacturing sites, businesses with workforces greater than 200, and more vulnerable groups.
Kirklees will test whole communities, starting in areas of persistently high infection rates and targeting high-risk workplaces.
Health Secretary Matt Hancock said he was "really pleased" to make the announcement after "the successful work" in Liverpool.
"With one in three people with coronavirus showing no symptoms, increased community testing is a vital additional tool at our disposal to help identify those who are infected and infectious, but unaware that they might be spreading the disease," Hancock said.
"Community testing will be very important in helping the areas where levels of the virus are highest to drive down infection rates and ultimately will help areas ease tougher restrictions," he added.
"This is just the start, and we are working quickly to roll out community testing more widely as soon as more local teams are ready. I urge all those living in areas where community testing is offered to come forward and get tested."
Hancock has attributed the result to residents following restriction rules and the recent mass-testing pilot in Liverpool.
The BMJ said that the lateral flow test can't rule out CCP virus infections due to its low accuracy rate and lack of knowledge of who is actually infectious.
Around 2,000 troops were deployed to Liverpool in November to help with the pilot. According to the LCC website, residents can visit a test centre or order a home test kit.
The BMJ also said that both scientists and politicians have mixed up having “high viral load” with being "infectious," a correlation it said was wrong.
"It’s still unclear how viral load and ease of viral culture from people with PCR positive results relate to level of infectivity," the BMJ said.
"Although evidence suggests that the virus can be more easily cultured from people with higher viral loads, it can also be cultured from people with lower viral loads. Also, detected viral load varies according to how much biological material is caught on a swab, and it is not yet clear whether SARS-CoV-2 can be spread when the virus cannot be cultured at all."
"If successful, this approach will be extended across the health system next month, and to the whole of England from January."
The DHSC didn't respond to a request for comment.