The plans include a three-storey building with six flats at 118 Canonbie Road in Forest Hill.
A two-storey vacant building at the site, previously a hostel, will be demolished if the proposals are approved by councillors at a planning meeting on Thursday (January 9).
The former hostel building has been deemed “not fit purpose”.
There are more than 7,000 people suffering homelessness in Lewisham, the equivalent of one in 43.
“The proposed development forms part of Lewisham Council’s programme to deliver 1,000 new genuinely affordable Council homes across the borough by 2022.
“Providing housing, particularly affordable housing is a current policy priority to tackle the housing crisis in the borough and wider London,” according to the planning document.
The plans, which are car-free, also include 12 cycle spaces and a large shared garden.
Residents in the area have raised concerns that the lack of parking provision could put pressure on current residential spaces.
In response, officers “acknowledged the proposal being car-free is of concern to residents”.
“The submitted transport statement proposes to submit a travel plan to encourage and support the use of sustainable transport at the application site.
“The travel plan would be secured by condition,” according to the planning document.
Officers said that an independent parking survey had shown a capacity for on-street parking within 200 metres of the site “to accommodate any parking demand generated by the development”.