Thanks for updating with your question. It looks like you might have some cross-over with Bethan, so please do keep an eye on the resources she’s looking at.
Here’s some interesting resources I pulled up. I think, from my very quick look, that official loneliness statistics is mainly at national level: Loneliness in Older People - FOI response
I did, however, find some interesting starting points to add to your search:
It is estimated that across the UK older population, 9-13% of people report being often or always lonely or are socially isolated (Age UK 2016).
I’m very interested to see what you find! Please add your reflections and findings to Resources for check-in #1 - Finding Data.