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And Labour’s Daniel Johnson says car parks which lie empty outside office hours could play a vital role.
The Capital currently has the second lowest number of charging points per head of population out of all 32 Scottish local authorities.
But Mr Johnson argues with the COP26 climate summit coming to Scotland and an increasing urgency about responding to the climate emergency, new initiatives are needed.
He recently held a virtual meeting with community council in his Edinburgh Southern constituency to discuss how best to increase electric vehicle (EV) charging provision.
He said: “It’s clear that there is a demand from constituents to move to electric vehicles but the charging points are in short supply across the city.
“Edinburgh needs to do so much better on this. The infrastructure just isn't there and if we are to properly move away from fossil fuels and achieve our climate goals this has to happen at pace.
“That will take government action and legislation but it is also, I think, incumbent on individuals and communities to think about what they can do.
“My effort is to see if we can have community-owned, community-controlled charging points in places which are not used overnight or outside business hours, whether that’s churches, schools, universities or elsewhere.
"Edinburgh has a lot of housing which does not have off-street parking so this would seem to be part of the solution.”
He said he had been exploring the possibilities of working with not-for-profit organisations who had helped establish community charging points in car parks in a wide variety of locations. “It strikes me there are lots of opportunities for that right across this city.”
Transport convener Lesley Macinnes said she welcomed moves to increase EV charging in Edinburgh.
She said: “Supporting the transition to cleaner, low emission vehicles is a key element of our City Mobility Plan and is one of a range of initiatives to improve air quality and achieve net zero carbon in the Capital.
"This includes encouraging the uptake of electric vehicles, both by residents and by businesses, freight operators and public transport providers.
“Over the next year we’ll be rolling out the first phase of our on-street charging network, with 66 charging points, totalling 132 charging bays, to be installed across the city, which will be crucial for many residents choosing to move to cleaner transport. This adds to a number of publicly-accessible charging points already located around Edinburgh, and we support any initiative to increase this further.”