Simple really: on a 1:25000 map the trails are marked in green. Short dashes are Public Fotpaths, where mountain bikes aren’t allowed. Long dashes are Public Bridleways, where they are. Crosses are Public Byways, where bikes are allowed; and long dashes with short green dashes dissecting them from alternative sides are Roads Used as Public Paths or RUPPS, which are legal on a bike but are gradually being phased out to be replaced with Restricted Byways, which will also be legal. You may also see green circles, which denote a public right of way, usually legal for bikes too.

The only other thing that may help is that sometimes footpath or bridleway dashes are orange, meaning they are permissive paths/trails rather than legal rights of way. This doesn’t usually matter much on the ground but occasionally there may be restrictions imposed by the landowner, and of course, the permission could be withdrawn.