Tommo, thanks for intro. Dear Heather, firstly there is no blanket answer to how to get councils to connect and then implement a climate action plan. However, there are some basics things we found made a difference to the campaign.
The first is position yourself (as you are doing) at a local4local level to get acceptance by council and the other community members. We formed a Social Responsibility Committee that has a sub committee of community cohesion - as some changes can alienate as well as bring people together for the greater good.
Step 2 find out what matters locally and what can be done. - councils like to have early and easy wins and after 20 years I am still amazed at how the little things are still not being done that could be.
So in summary get a local action plan sketch together, get some other people on board, but my advice would be to pick a positive name -‘bright future’ Our space Our Environment etcetc that stops the "oh another green bashing group’ - this is still a hearts and minds campaign. Then the hard bit - do the councils job for them find some problems or changes and work out how they can be implemented.
As far as engaging with council, local councillor is worth the courtesy of contacting, but usually there will be a cabinet member for carbon /environment and a team to approach but at the same time get the inward investment officer and get him to understand clean air and good management of resources is attractive to business and families and a good examples of eco homes, waste recycling, or even just information sharing can lead to new jobs.
Pollution is simply poor efficiency - reduce pollution increase efficiency and even to skeptics they all know higher efficiency is more $$$ - I always like to show them that done at a scale that makes a difference, they can save or make money too - it is still sadly the biggest motivator for the decision team in a council, and without it they can do nothing. - hope it helps