CANAL TOW-PATHS As of right, that is. However, many towpaths are now being made into cycle ways. In some parts of the country, cycle permits are necessary although these are normally easy to obtain, albeit for a fee.
CTC are *excellent* on cyclists' rights of way and cyclists' rights in general.
Although it sources from an alarmingly elitist clique of recreational cyclists who never seem to let anyone sign up to their private forum this sounds like a great code of conduct for cycling 'off piste' should one choose to do so.
Sites of Special Scientific Interest should be recognised as such: personally, I wouldn't want to disturb nesting birds, crush rare sphagnum under my tyres etc.
Bicycles are great fun and they've got me round many, many ancient sites. Albeit beetroot of face and collapsed of lung.
I always tend to apply Scottish land right laws throughout the UK as they're far more sensible than the English and Welsh ones. It's rare that anyone really minds.