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Equestrians and cyclists are vulnerable road users. Both groups share similar risks when riding on the road and both need access to more safe off road riding.
Cyclists and horse riders have a statutory right to ride on byways, bridleways and roads. On bridleways, it is important that cyclists give way to horse riders (the Countryside Act 1968 gave cyclists the right to use bridleways, but stated that they must give way to horse riders and walkers).
http://www.horseaccidents.org.uk/Advice_and_Prevention/Cycles.aspx