It comes after a new broadband cabinet was installed outside the Christian Science Society in Coleham, but the church complained that it blocked its noticeboard and asked for it to be removed.
The cabinet was removed days later and then residents complained that Coleham is one of the few areas in town waiting for fibre broadband to be enabled.
Jacky Sinclair, chairwoman of the Christian Science Society board, said they were keen for fast broadband to be available for residents, but the information box was impossible to reach behind the cabinet.
She said: "We are keen for broadband to be brought to the area and to support our neighbours' activities.
"However, putting the box in front of our notice board was apparently a quick decision made when it wouldn't fit in the intended location.
"It was impossible for us to reach the board safely to change the contents.
"We offered a piece of our land rent free and without restrictions for the re-siting of the box, but this offer was not taken up."
A spokesman for Openreach said that finding a suitable location had been "extremely difficult" and that the company has to balance their responsibility to carry out work with the views of residents and community groups.
The spokesman said: “We’ll be taking another look at this in the future, and people should monitor openreach.co.uk for the latest updates."