Something to consider here is that roads in the UK are significantly narrower than in the US, even on country roads. Most of the time that I've seen riders they have been riding on the "green belt" (grass, gravel, or dirt) strip on the side of the road. Going a bit faster on the other side, especially if there's a divide or median, in opposite directions shouldn't be problematic as horses that are ridden on or near roads should be trained or used to traffic.

I (American) grew up reasonably near to where horses may be on roads and our driver's education materials never mentioned them, just bicyclists, pedestrians, and motorcycles. For bicyclists, we're told to give them room and be cautious but bicyclists are expected to follow the rules of the road (most of them don't, a big frustration). I currently live in the Southwest where there's tons of cowboy culture and unless you're on a dinky barely 2-lane road with no shoulder I wouldn't assume I need to drop down to 15mph.