Twenty-three cases of Covid-19 have been traced to birthday celebrations and members of an extended family visiting each other indoors.
Contact tracers are worried there could be more cases as some tested have not wanted to share details of contacts.
Of the known cases 22 are in Neath Port Talbot while the other is in Swansea.
Swansea Bay health board said people in Briton Ferry, Cimla and Resolven - all in Neath Port Talbot - with symptoms should be tested immediately.
The health board's public health director, Dr Keith Reid, said: "We're aware of an extended family and friends who have apparently been going in and out of each other's homes, which is not currently allowed.
"Being so familiar with each other, there has also been little or no compliance with social distancing, wearing facing coverings, et cetera, which has increased the likelihood of the virus being passed on."
He urged those testing positive to "be open and honest with the tracing team".
Dr Reid said: "Details remain confidential and are used for contact-tracing purposes to stop the virus in its tracks.
"We know that the majority of people do stick to the rules, and we thank them for their patience and cooperation.
"But we are not out of the woods yet.
"The numbers of positive cases in the Neath Port Talbot and Swansea areas have started to go in the wrong direction again, and it's everyone's responsibility to ensure they come back down."
The rules existed to "safeguard people and slow the spread" of coronavirus, he said.
"A significant number of cases now are down to household gatherings which should not be happening in the first place," said Dr Reid.
"You might think that because it's your family member you're meeting up with that it doesn't matter, you couldn't infect each other.
"But that's wrong, and a totally false sense of security.
"The virus doesn't care if you're related. In fact, it thrives on close contact. Which is why we're now dealing with this cluster in the Briton Ferry area."