City Lofts, St Pauls apartments overlooking the Peace Gardens, will have the new cladding.
The work will cover the 11 storey building on St Pauls Place and a 32 storey building on Arundel Gate, which were constructed around 2009.
Residents in the 316 apartments are aware of the issue and will remain at home while the work is carried out.
Halliday Meecham architects say in a planning application: “The proposed works are required following a client commissioned fire risk assessment identifying that the existing building is over 18m in height with combustible materials used in the external facade.
“The client has identified a need for a full cladding replacement scheme and commissioned a series of fire risk assessments.
“Surveys and investigations have confirmed the external wall cladding contains combustible insulation and there are limited areas of fire breaks that limit the spread of flame in a fire scenario.”
The application says the combustible insulation is bonded to panels which are difficult to remove and easily damaged so will be replaced.
The new cladding will have “appropriate certification by a qualified fire consultant” to confirm it meets regulations and is fit for occupation.
The replacement cladding will match the existing materials so there is “minimum visual impact on the external appearance of the building” and to conserve its setting in the city centre conservation area.
The application adds: “A team was appointed in late April 2021 to develop the design and have been in regular contact with residents to discuss the project and remedial actions.
“The works are focused on removing existing defective materials and reinstating new non combustible materials in the same configuration and of an identical appearance.”
City Lofts has applied to the Building Safety Fund, a Government scheme which is providing £1 billion to support the remediation of unsafe cladding on residential buildings 18 metres and over in both private and social housing.
Full details on the application can be viewed here