This is common law nuisance and the neighbour is under a duty to keep animals under control. Ironically, it doesn’t apply to cats.
However you cannot beat the neighbour with a stick until they fenced the chickens in and if they will not respond to written requests to do so, then you have no alternative but to make an application to court for an injunction to compel them to fence them in.
That really is all there is to it except to say that you would also be entitled to claim the cost of putting right any damage caused by the chickens.
You may find that a strongly worded letter from a solicitor threatening a court application and an application for costs, may focus the mind without actually the need to get to court.
Check your house insurance to see if you have legal expenses cover that would pay for the legal cost of taking this to court.
Can I clarify anything else for you?
I am happy to answer any specific points arising from this.
Please take a moment to look at the top right-hand corner of the page and rate my service by clicking one of the stars at the top of the screen.
You may need to login again to use the rating service.
It's important that you use the rating service because that gives me credit.
It doesn't just give me a pat on the head! It's what gets me paid!!
There is also an experts incentive scheme whereby the more 5 star ratings I get I do actually get a pat on the head!
All you need to do is press Submit.
If you still need any points clarifying, I will still reply because the thread does not close.