Thanks for all the responses. Let me try and answer them here.
Cats - I’m working on that. More convincing to do
I’ve seen some droppings in the loft.
My LA doesn’t offer any pest services. They refer us to local companies.
I also live in the countryside and we back into some fields. It’s a normal occurrence to see mouse running across the garden every once in a while. I’ve also got a raised patio and have seen a few burrow their way into that. I don’t see how they get from here to my loft. It’s a double storey house.
I was planning on making a concerted effort. Use the spring traps and water bucket contraption (seen on youtube!) outdoors. I wanted something more sophisticated in the loft as its lot the easiest place for me to get to. I was thinking a multi-kill trap that keeps them in the device but alerts me when the deed has been done. If these things are reliable, I can keep it up there and it can spring into action even after I’ve dealt with the problem more holistically.