The railway, which has ferried people from Low Town to High Town for more than 130 years, had to be closed before Christmas on health and safety grounds after structural issues were found with a retaining wall at the top of the attraction.
Following its closure, 14 out of 16 staff who worked at the railway were made redundant.
Since then, Bridgnorth Town Council has been ascertaining who is responsible for the wall in a bid to ensure repair work can begin.
Earlier this month an application was made to Shropshire Council to close Castle Terrace at the top of the railway to allow repair work to commence but so far there has been no activity.
However, Clare Turner, Town Clerk of Bridgnorth Town Council has said remedial work is to begin on Monday.
She said: "After an extensive review of the various leases in relation to the relevant areas at the Cliff Railway, as well as investigations by a specialist engineering company and land surveyor, our legal advisors have notified the Cliff Railway’s operator of the council’s intentions regarding the retaining wall."
She said that while "it would not be appropriate to go into detail at this stage", she added: "Constructive dialogue with the operator has taken place and we are pleased to inform that the Castle Walk will be closed from March 27 to allow this remedial work to start.
"The works will begin with scaffolding being erected to allow the contractor to access the area safely and still allow the regular maintenance to continue."
Owner of the Bridgnorth Cliff Railway, Malvern Tipping, has been approached for comment.