[Hi there, I used to work in estate management so I can tell you what I would have responded best to!!
Managers / keepers are generally (!) busy people so it is probably best to write a letter rather than phone or drop in. Make sure its polite, with proper spelling and grammar! It might sound basic but 4 out of 5 letters we used to get were dreadful. Explain that you are very interested in getting into gamekeeping once you leave school and are very keen to do work experience with a game keeper. If you have experience with dogs / ferrets etc or otherwise working outdoors say so - and a