Programme producers are researching new locations but confirmed cameras will not be returning to James Turner Street in the Winson Green area.
In a statement from Channel 4, a spokesman said: "The first series ignited an important debate about the welfare system and we are interested in seeing if we can revisit this through the experiences of residents of a street in a different part of Britain."
The show, which follows a series of people living on benefits, has been a ratings hit for Channel 4 but has been criticised for allegedly demonising those living on the breadline, while some of the residents claim they were misled into appearing.
With the airing of the last episode in the current series this week, local MP Shabana Mahmood has written to the boss of Channel 4 asking his company to fund community measures after claiming that filming had blighted the area.
She has asked channel chief executive David Abraham to fund street wardens, who she believes would help keep the area clean, tidy and safe.
Ms Mahmood claimed residents of the street in Winson Green were "completely fed-up".
She said they were being blighted by "TV tourists" paying visits to the area, and also claimed children of some residents who appeared on screen have been bullied.
Ms Mahmood said one house in the street had been "egged" and one of the street signs was daubed with graffiti over the weekend.
Calling the broadcaster to account, she said: "Channel 4 has created this problem, they need to help fix it."
In her letter to Mr Abraham, the Labour MP for Ladywood wrote: "Children have been bullied at school and at least one child is almost too scared to go out of the house.
"The impact of this on residents cannot be overstated.
"All residents are completely fed-up. Some are very frightened - particularly the elderly and the young.
"Hundreds of people are suffering, almost all of whom did not want any part in the programme which they quite understandably feel portrays our area in a negative and inaccurate light.
"The police are giving the support that they can but resources are limited.
"I am working with them and the residents to help set up a neighbourhood watch group in the area."
Ms Mahmood has said street wardens could "provide a friendly but strong security presence for residents".
Channel 4 said it had been in contact with West Midlands Police about residents' welfare, and had also already spoken to Ms Mahmood, councillors, the local school and other community workers in the area to discuss concerns.
It did not directly respond to Ms Mahmood's request to fund wardens for the area.
After the first show was broadcast earlier this year, viewers complained about alleged criminality by some of the residents, which prompted West Midlands Police to issue a statement saying its officers would be monitoring the series.
Some of the residents appearing in the show have claimed they were misled about what the programme would involve - a claim Channel 4 has denied.
The show has prompted a public debate on wider issue of people living on benefits with Deputy Prime Minister Nick Clegg saying he believed a discussion needed to be had "about what sort of welfare state we can afford".
Mr Clegg made his comments on a radio phone-in show he co-hosts, three weeks ago, after one of the programme's unlikely stars Deirdre Kelly - known in the programme as White Dee - rang in.
She claimed the series had been "very cleverly edited" and suggested residents were misled into appearing after initially being told the show would focus on "community spirit".
Ms Kelly said at the time: "The programme has been a shock and no way did we ever think it would be this big."
Meanwhile, in a statement, Channel 4 said: "If any residents requested not to be filmed, they were not.
"The contributors were briefed extensively before any filming took place and have been given support all the way through the process - members of the experienced production team have been in regular contact with them.
"The main contributors have been offered the opportunity to view the programmes they feature in before transmission.
"We took on board their comments and in some cases made changes to the programmes."
A spokesman for the channel added that production company Love Productions and broadcaster "followed strict protocols in accordance with the Ofcom broadcasting code" in relation to filming children and had obtained proper adult consent where required.
"At the request of the production team, featured contributors also informed the school of their children's involvement in the series," the statement continued.
"The production team made the local school aware of filming on James Turner Street from early on in the shoot.
"Since the programme has been on air, both Channel 4 and Love Productions have been in contact with the school's new headteacher to offer support if required."