Mouse House

Maintenance

I have reached stalemate with a tenant complaining about mouse infestation. I wonder how you would handle this?
The tenant reported seeing a mouse in the house so I went round the next day. I spent an hour with the tenant going round the house and agreed my builder would fill in 3 holes in an exterior wall. I offered to pay for the poison and traps he had bought and gave him a mouse trap of my own and some steel wool to fill any holes he found on an emergency basis. 3 days later my builder took a bucket of mortar and filled the holes agreed plus numerous other tiny cracks in the external and internal walls for his peace of mind. And I agreed to a £50 reduction in that month's rent because he claimed to be sleeping at a hotel. One week later the tenant phoned me in a panic saying he wants the bath panel sealed because mice can get through and he wants the kitchen bas units taken out and refitted because one unit has a back panel bowed out of its groove. And holes in those base units for pipes he wants filling in. I refused to do any of those things because I think my responsibility is with the external structure and kitchen units and bath panels are not designed to stop mice. He has sent me a video showing what he thinks are the defects in the kitchen units, which I think is not relevant. I have said if he can show me more holes in the outside wall I will fill them. But he has shown me none and so I rest on my last maintenance inspection last month until he shows me something new. He has shown me no actual mice. He has shown me a photo of one set of mouse droppings (possibly).
He has stopped paying rent. I have served s21. I am not worried about losing this tenant but I want to make sure I do the right thing about the infestation. I think the house is in excellent condition, floors are solid and kitchen units are perfectly good enough.
Should I do more?
He says he will get an expert in and I am encouraging him to do so....