Maz said:
I occasionally have to overtake a horse and rider on my way to work.
What's best to do? Just give them a wide berth? Do you speak to the rider when you're still behind them to let them know you're about to overtake?
Yes, speak, gently, but audibly from a little way back (so don't suddenly holler from just behind them). That way, the rider knows to expect you, and the horse knows you're a human being (as opposed to a random predator). I'd generally say "hello, cyclist passing" in a cheery tone and then pass steadily and with a wide berth. Think how you'd like a car to over take you, then apply that to yourself basically. I don't think I'd wait for permission necessarily, unless I was leading a big group, but if a rider asked me to wait or hang back while they pulled over, I'd do so. If on the recumbent, I'd be extra cautious, since horses tend to be even less used to recumbents, which have a rather predatory shape, and often a flappy flag.
On the rare occasion I'm out on the road on a hack, I find my awareness is similar to being on the bike - by half-glancing back frequently, and listening, I'm well aware of cars and motorbikes, less so of cyclists.