Greenwich Council will no longer be considering the areas as part of the Sustainable Streets scheme, with the focus instead being placed on the areas that could benefit the most.
The consultation for the areas will now be closed, with no permit parking proposals put forward.
This decision will not affect existing controlled parking zones (CPZs) in the areas.
Councillor Averil Lekau, deputy leader and cabinet member for climate action, sustainability, and transport, said: “We keep our proposals under constant review.
“Therefore, we have reconsidered our Sustainable Streets proposals and are adjusting our consultation to focus on the four areas we think could benefit most from the Sustainable Streets scheme (Charlton, Kidbrooke and Blackheath, Thamesmead West, and Woolwich) where they are either town centre locations with good transport links, have high levels of new development, or areas that would suffer from parking displacement from other areas.
“This means we will be withdrawing the proposals in respect of Shooters Hill and Plumstead areas.
“The consultation in respect of these areas is closed and we will not be bringing forward permit parking proposals in these areas.
“This will have no bearing on already existing CPZs in those areas.”
The in-person events at Woolwich Town Hall for August 20 (Shooters Hill) and August 21 (Plumstead) have been cancelled, and those who had registered to attend or who were on the waiting list will be notified.
The remainder of the consultation for Charlton, Kidbrooke and Blackheath, Thamesmead West, and Woolwich will carry on until September 30.
Town Hall events will take place on August 12, 13, and 19, for Charlton, Kidbrooke and Blackheath, and Thamesmead West, respectively.
An online webinar will be held on September 29.