May I ride a motorbike through a non strictly forbidden trail? Do I need some specific permission?
Without specific permission from a land owner the only type of trail you can use is a Byway. These are strictly speaking roads, but tend to be used primarily for recreation by the public, and are generally maintained as farm tracks. Some are designated as a restricted byway that do not allow powered vehicles.
Byways are shown on Ordnance Survey Explorer maps as a long dashed green line, and as a long pink dashed line on landranger maps.