Those doves are actually not doves, but pigeons. The ones they use the most over there are garden fantails, which are a mix of homer and american fantail. They look like fantails, with a bit more of a cone shaped tail, normal stance, and have a bit better flying ability. If they were doves, they wouldn't be coming back
To get them settled into the dovecote, they put a net around it that goes to the ground. The birds learn to roost in the little house, eat, and drink there as well. Because they are pigeons, they have the natural instinct to come back home by the end of the day. So the birds, after being kept in for about a month, then stick around the yard. They are in great danger of predators, which is why most people around here don't do it. Most people I've heard of in the UK doing this, are in or closer to the city, where hawks may not be a huge problem. Cats however, are probably a larger problem for them, which is why their dovecotes are up on poles.
My birds are allowed to exercise and roam around twice a day, but I keep them under control by having them on a feeding schedule. The longer they are out, the more of a chance a hawk will attack. We live out in the country, surrounded by trees, so it doesn't take long to attract those boogers. I have let my birds have open loft days, in which they spend all day going and doing as they please. But I always waited to feed them, so that if anything came up, I could easily get them back in the loft where it's safe.