Westminster Council has applied to its own planning department for listed building consent to erect the bronze plaque on the Transport for London-owned bridge.
The plaque will carry the names of Kurt Cochran from the USA, Aysha Frade and Leslie Rhodes from London and Andreea Cristea from Romania who were fatally injured on the bridge on 22 March 2017 and PC Keith Palmer who was killed a short distance away in New Palace Yard.
Fifty people from the UK, France, Greece, Germany, Poland, Portugal, Italy, China and South Korea were injured.
"The centre of the south parapet of the bridge was chosen for the site of the proposed plaque as it was along this pavement of the bridge that the four people were killed, two on the west side and two on the east side, before PC Palmer was killed in New Palace Yard," wrote Tony Andrews, the City of Westminster's emergency planning manager.
"The central location best memorialises all of the victims. (There is of course a separate memorial stone for PC Palmer outside the Houses of Parliament).
"People standing to read the plaque overlook the iconic sites of the Houses of Parliament to the right and St Thomas' Hospital to the left (where many of the injured people were taken)."
The council says that the position of the plaque on the upriver bridge parapet "allows pedestrians to pause and read the inscription without blocking the pathway".
According to a letter submitted with the listed building consent application, the plaque is supported by the families of all the people who died, as well as a group of survivors.
The plaque installation is also said to have the backing of the Lord Mayor of Westminster, the Mayor of London and the Speaker of the House of Commons.
• See application 21/00780/COLBC for further details.