Nobody wants the swimming pool closed just an acknowledgement by the Council to local residents that their justification for not providing parking "We expect all users of the swimming pool to use public transport" was wrong and they should work towards reducing the impact on local schools and residents of the pollution it causes. There are many ways this can be done but the first step is acknowledging the pollution and working from there with some carrot and stick policies.
You can do both, have a high charge for the most polluting cars and for expensive EVs. The government in the latest budget is phasing in road tax for EVs with many of them also being caught by the expensive car tax rate. Lewisham should do the same now.