If you are going or thinking of going onto private property to shoot then yes you do need permission from the owner, although thats frequently easier said than done. Most of the time, I doubt you will find the owner, so if not, respect all property, don't cause any damage, don't scare any farm animals, etc and if the owner does turn up mid shoot, explain why you are there and ask if he would allow you to continue.
Most of the time though I doubt you will be disturbed or encounter any problems.
It really depends what you're shooting and what you want to do with the shots.
If you are walking a public right of way and taking a few snaps of friends or family then obviously you don't need anything. At the other end of the scale, if you were shooting a major advertising campaign it would be sensible to have paperwork in place. If any shots are for personal use only then it is unlikely that you need to bother. You may be chased off if you intrude into someone's private property. The clearer it is who owns the field, woodland etc,the more likely it is that it would be appropriate to seek permission.
The situation may be somewhat different in the USA both legally and practically (shooting people seems more acceptable there) so any article written there will not be generally applicable here.