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Different Local Authorities chose to describe it in different ways either as a footpath or as a bridle way (which almost always allows bikes) when they were making their List of Streets or Definitive Map.
There was no real national policy.Since the NERC 2006 Act of Parliament you can’t grant higher rights -footpath to bridle way or road.
Our Rights of Way laws have developed piecemeal mostly starting with the Enclosure Acts but The Ridgeway predates even this so the real answer to your question is God knows why.
Can anyone explain why you can ride most of the Ridgeway west of the Thames, but the majority of the eastern section is considered a footpath? Apologies if this is a dim question.