Yes, Ivan, this is one of those weird things about English, but it is in fact regarded as very good English to say it just like this :-) . Chasing the animals to the bottom of a field (or running down to the bottom of the garden) simply mean that the animals were chased to that part of the farm furthest away from the farmhouse (or the part of the garden furthest away from the house), so right to the very end of the farm, as it were.
One can even talk about going down to the very bottom of a country, which would mean its southern-most point.
Enjoy the book. It's a fantastic read!