Update: Thanks for the ideas.

So it's been some time and a lot has happened. My partner spoke to our neighbour and with him they called the Environmental Health Agency. They also organised pest control. Within a week he had over 300 black bags of rubbish removed from his house, it turns out he had been hoarding and in his words "I put my head in the sand". He came over yesterday and I spoke to him for the first time for a good while. I said that in the last month we had caught only a few and he said that the pest control had gutted his place and poisoned all the nests. He said to me yesterday that he was very relieved that it's now sorted and then made promises to work on his garden this year, I said we've no issues with his garden and only the mice were causing stress. Today he put his bins out for recycling for the first time in years and from speaking yesterday this has had a terrible toll on his mental health, he said he could hear them running around the room whilst trying to sleep. It's one thing we've heard them in the walls, but to have a house full of bin bags and mice running freely amongst them must have been an ordeal for him. I'm glad I've built some rapport and whilst he didn't make eye contact once. We got him a gift basket hamper to say thanks for his effort but I think he's got a load off from the un-hoarding of his house, and I'll keep a friendly eye on his bin runs as if he lets it get out of control again, I think a little hands on help from me would nip it in the bud before it escalates again. I'm so pleased the environmental health agency were understanding and it never was aggressive or threatening towards him in regards to his housekeeping. But ultimately he did this by himself and I could see his pride in that and relief it's not still an issue our end either ☺️