Yes of course, the wealth of bridleways in Sussex too - the South Downs Way is probably the best known. I don't MTB myself, so when I'm on the SDW it's always on Shanks's pony - but I meet a lot of cyclists and equestrians there. I don't think there's any conflict although both riders and cyclists do need to exercise a fair bit of etiquette when there are lots of walkers. For the four-legged contingent, going at a gallop or even a canter is definitely out.
I do recall one horse rider going at full gallop along the South Downs Way on a busy Sunday, scattering angry walkers in his path - but it turned out that it was an emergency. Someone else had had a heart attack further along the path, and the rider was racing to the road to meet and guide the paramedics. Normally riders play by the rules.
I do recall one horse rider going at full gallop along the South Downs Way on a busy Sunday, scattering angry walkers in his path - but it turned out that it was an emergency. Someone else had had a heart attack further along the path, and the rider was racing to the road to meet and guide the paramedics. Normally riders play by the rules.

) I was rapidly velocipeding along the B1040 between Crowland and Thorney whenI happened upon a group of racehorses out for their morning exercise. I now know that a lady called Pam Sly, who's horse Speciosa won the 1000 guineas at Newmarket four years ago, has her stables along here, but didn't then. Neither did I know how to approach horses from astern, so I crossed to the opposite side of the carriageway (very quiet road) but did not slacken speed or call a warning. As I passed the lead horse of the group I could hear the clatter of a shying horse behind me. To my shame I neither slowed or looked behind me 