I don’t want rats in my garden, which I believe is quite reasonable
It absolutely is. And I agree with the sense of revulsion you describe as well.
I am a lover of wildlife, and believe that we shouldn’t kill anything at all unless absolutely necessary – and even then, never ‘happily’ – but sometimes other creatures invade space we need for our wellbeing, and they have to be dealt with in the most effective way possible.
We once had a mouse invasion, and had evidence that they had got all over our kitchen, and even into one of my infant child’s cot. That’s when my ‘live and let live’ approach went out the window.
Your garden is your living space. There is an invasive, malignant creature in your living space. Learn how to shoot an air rifle and get rid of it. Or look around to see if Wiltshire has a group of people with terriers who will bring them ’round with the purpose of sorting out the problem. I’ve heard of such programmes in Norfolk.
[P.S. Yes, sure, birds can carry disease, but rock doves don’t present much of a danger when I go outside, and they certainly haven’t tried to move into my house. Rats can do both.]