The new rules will apply to Westgate Road and Westmoat Close.
They form part of a legal order made by Bromley Council on August 27.
The changes will affect both sides of Westgate Road between its junctions with Foxgrove Road and Beckenham Place Park.
On Westmoat Close, the restrictions apply to the entire length of both the north and south sides, from their junctions with Westgate Road.
In addition to the new permit parking requirements, the council has also amended waiting restrictions on Foxgrove Road.
The single yellow line on the north side of Foxgrove Road, opposite houses 38b to 40, will now operate from 9.30am to 2.30pm, Monday to Friday.
This replaces the previous restriction, which was in place from 8am to 4pm.
The affected stretch of Foxgrove Road runs for 57.13 metres westwards from a point 31.25 metres from the western kerbline of Westgate Road.
The orders have been made under the Road Traffic Regulation Act 1984.
Full details, including exemptions for certain vehicles and persons, are contained in the original order.
Copies of the order can be inspected during normal office hours at Bromley Council, Churchill Court, Westmoreland Road, Bromley, BR1 1AS.
They are also available by emailing TrafficManagementOrders@Bromley.gov.uk until six weeks after the date the order was made.
Anyone wishing to challenge the validity of the order on the grounds that it is not within the powers of the enabling Act, or that any requirement of the Act or relevant regulations has not been complied with, may apply to the High Court within six weeks of the date the order was made.
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