Neem is one of natures wonders. I have used it for many years.
I would dilute the Neem with 2tablespoons each of Neem and liquid soap to a gallon of warm water and wash the horses all over with that. Severe cases like sweet itch, I would use it neat on the ultra sore parts.
As for eyes, I do not think it is risky, I would bath the dogs in it and sponge them all over, never harmed their eyes.
I use a more dilute mix in a backpack to spray the garden for ridding plants of pests.
I have used it neat on a very serious wound in a horse's side to prevent proud flesh.
When I had a severe skin issue I used it in cream form and it did alleviate the itching.
I think that some of the bugs you get that side of the pond are way worse than in the UK so, doubling the mix to four tablespoons of soap and Neem would help more.