Note: I'm not from the UK, but a quick search of the laws relating to poaching is pretty easy.
Note: THERE ARE MANY ANIMALS IT IS ABSOLUTELY FORBIDDEN TO HUNT/SHOOT (think large large fines and jail time). Always identify your target.
The short answer is: Yes - it's illegal apart from under certain specific circumstances.
Poaching is illegal. Poaching is defined as the illegal taking of animals and plants from the environment. Many traditional hunting/shooting sites are on private land, and it is considered poaching to hunt/shoot on these lands without express permission of the land-owner. It is also considered poaching to shoot animals owned by anyone (e.g. someone's sheep or cow). It is also considered poaching to harvest (at least some) wild plant species and many marine/aquatic species. Poaching also encompasses not having a hunting/shooting/fishing licence for the species caught/killed.
There are only certain animals that are allowed to be shot/hunted and even for those there are closed seasons where shooting/hunting are not allowed at all, or only in limited numbers (certain number of animals/person per day or [hunting] season etc). Open seasons and bag limits vary according to the species being targeted, and where you are in the country. You are also required to have a licence to hunt/shoot for the game species being targeted.
If you are caught poaching, it means large fines and/or jail time!