Developer BexleyCo Homes wants to build 33 homes on the site at 89 High Street.
Part of the façade of the existing building, which is locally listed, would be retained, with the rest demolished.
Two new shops would also be provided as part of the scheme, as well as a roof terrace for residents.
The site contains Erith Post Office, as well as the former Sorting Office and yard.
The developer said: “Retaining both the south and east elevations, which contain almost all of the design interest of the building, would retain almost all that gives the building its character.
“Private, street-facing entrances for several ground floor apartments and town houses.
“This enhances street activity and provides natural surveillance for the surrounding area.”
Three-quarters of the homes built would have two bedrooms. Eight flats would have three bedrooms with the remaining home being a single-bedroom flat.
At its tallest point, the new building, which sits at the junction between the High Street and Bexley Road, will be six storeys high.
The development would include 31 flats and two townhouses, both of which will be three-storeys high.
Bromley Council is yet to decide on the planning application.
