People in the town of Beccles on the Norfolk\Suffolk border say the peacocks were destroying gardens and even damaging cars.
Local councillor Graham Elliott says he has received lots of calls from people complaining about the birds.
"The numbers are increasing," he says.
"The damage might seem small scale but it's persistent it can be very significant for people," Elliott was quoted as saying by ITV.
He thinks there are about seven roving round the town. So far, the birds have resisted attempts to catch them.
"When we first moved here they were in the garden four or five times a day, every day so that was quite hard because they can do an awful lot of damage. It's the wrong environment for them. It's not their fault. They need to be on an estate somewhere," Goodwin said.
If the peacocks can be rounded up, a local farm is happy to take them, the report said.