Thanks for the OP and big thanks to shysal for the link. It's pretty clear one of our neighbours has the occasional grey squirrel cull, but currently there is one especially pesky visitor. He (maybe a she) skips through the leylandi our neighbour planted at the border of our gardens, and next appears on the roof of our shed. He stands up, little white chest gleaming, as he makes sure the dogs are not in the garden. Then, hopipty skip, he's enjoying the seeds in the squirrel proof (ha) bird feeders.
The other problem is some apparently genetically modified pigeons, who consume vast amounts of bird seed. The dogs dislike them almost as much as the squirrels. But, I can't let the dogs feed their prey habit by guarding the garden from squirrels and pigeons - the barking would irritate the neighbours.
So - I'm off to order on the link