Climate change impact / risk assessment
The UK Government already publishes information on this at the national level, which may be a useful guide for how to proceed at the local government level.
The last UK Climate Change Risk Assessment was published in 2017 and the next one is imminent in mid-2021.  They follow risk assessment methods set out in things like the HM Treasury Green Book, which, despite the name, is not about environmental assessment specifically (there are Orange, Aqua and Magenta Books too).  The Green Book
has a shorter, climate-specific supplement that may be a good place to start.  In particular, Annex B of the supplement has lots of links to other resources and tools for doing the assessment.
There’s also a local government website that hosts a slightly random selection of plans that various regions have put together over the last few years.
This all looks like a daunting amount of paperwork to a scientist like me, so good luck!