Members of the Labour-controlled borough are due to consider the call for the review at a full council meeting tomorrow, after eight Conservative councillors put forward the motion.
The motion states that the authority "regrets long-running problems in the planning department, including the significant processing backlog that emerged during 2016, and which despite the best efforts of officers who are working extremely hard, has still yet to be cleared more than a year later".
It says the council "further regrets recent planning errors that have led to unwanted applications going ahead, including for a William Hill on Plumstead High Street and a telecommunications mast on Siebert Road".
The council’s actions dealing with the William Hill betting shop application "attracted severe criticism" from the Planning Inspectorate, the motion says, which described the borough’s "clear, abject and repeated failure" to present evidence to the applicant’s appeal.
The causes of the problems, according to the motion, include "too large caseloads to properly manage and ensure quality assessments and decisions, an absence of performance management including coaching and mentoring staff" and "an absence of good practice which leads to officers doing their own thing and duplication work".
The "severity and continuation of these problems" led to Greenwich spending up to £50,000 in August 2017 on hiring "external consultants at £45 an hour to clear the application processing backlog".
A "service improvement plan" has been put in place, which includes the recruitment of an additional officer, "at further cost to the taxpayer".
The motion urges the council’s deputy leader to launch "a full review of what has gone wrong and why", which should cover the backlog and delays in processing applications; the recent "planning errors"; its planning enforcement performance; and "the steps needed to avoid continued and repeat problems from occurring".
A report on planning processes and procedures that will be considered by the council’s regeneration and transport scrutiny panel at the end of October, the motion says.
A spokesman for the borough said: "The government has set a performance threshold of 70 per cent for processing planning applications within the specified timeframes.
"We’ve worked hard to improve our planning department and deliver an excellent service which residents expect and deserve - for the period July to September 2017, 98 per cent of cases were dealt with by the council on time.
"We are committed to doing the very best that we can to listen, record and act on residents’ views for each and every planning application.
"We have apologised to residents where mistakes have been made and are working hard to make sure that such errors do not happen in the future."
The motion can be found here.
NOTE: this story was amended at 6pm on Tuesday 17 October to add a comment by the Royal Borough of Greenwich