As in any industry there are good practices and appalling ones. Some shoots are well managed with stocking densities more in line with natural levels. However even the Game Conservancy Trust, the professional association / lobbyist think stocking of 1,000 birds per hectare and culling any wildlife which might compete with the birds is not only acceptable but sustainable. http://www.gwct.org.uk/education__advice/gamebird_management/gamebird_releasing/1188.asp. Remember when reading it that this is considered 'best practice' in the industry. Many shoots ignore it. This is a typical thread showing the problems overstocking causes for farmers, let alone local wildlife. http://farmingforum.co.uk/forums/showthread.php?t=40817 This is an old article, but it summarises the issues, which still hold true today. http://www.guardian.co.uk/uk/2002/oct/07/ruralaffairs.hunting
If you are only feeding your chickens corn this is likely why they arent laying well, they arent getting enough protein. You need to add some pellets or mash, but not fish meal. Lack of access to fresh clean water can also be an issue, especially during freezing weather.