The development is intended for a vacant lot on London Road, between two current flat blocks Shelley House and Keats House.
The plans are for a three-storey building containing three self-contained flats – two two-bedroom and one three-bedroom.
Cycle parking and refuse storage facilities for the proposed flats is also planned.
Access to these flats will be from ground level, via the front of the site and the existing footpath to the west of Shelley House.
The site currently a lawn area in front of Keats House and to the west of Shelley House.
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The proposed development would be car-free, according to the plans, as it is close to Crayford Rail Station, and has numerous bus routes that pass London Road.
A daylight and sunlight assessment was presented alongside the proposal.
This assessment determines whether the additional build could cause a significant reduction in daylight or sunlight to the neighbouring properties.
The report shows the proposed three-storey building, due to its plot next to two current flat blocks, could cause a minor reduction in sunlight to neighbouring windows and gardens.
However, access to sunlight and daylight for neighbouring properties is still expected to fall within acceptable guidelines.
Comments submitted to London Borough of Bexley showed that 75 per cent of people who made a comment objected to the plans.
The application was submitted on behalf of Nirlake Investments on Wednesday, January 3, with the plans still waiting on a decision.