The English countryside is the setting for Daisy's adventures. Where exactly? We have no idea beyond that it's a drive or bus ride of indeterminate length (Daisy falls asleep en route) from the London airport.
The early part of the book takes places in Aunt Penn's rustic mansion, which is "practically falling down, but for some reason that doesn't make any difference to how beautiful it is" (1.3.7). The house is surrounded by a secret garden, fields of crops, and hills for animals to roam, and the barn is a short walk away.
The house itself sounds like every mystery-loving kid's dream, with "funny corridors that don't seem to lead anywhere and tiny bedroom with slanty ceilings hidden away at the top of stairs" (1.3.9). Down the hill in one direction is a small unnamed village, and elsewhere nearby is a river that connects to other parts of the countryside.
Piper and Daisy eventually get sent to live in a house near another village, and then a barn, and then slowly make the journey back toward the original house. For all intents and purposes, however, these places are indistinguishable from the part of the countryside where the cousins grew up, save for the feelings of family and home. Despite the sense of wandering through the wilderness on their journey home, in reality their trip seems quite civilized, with footpaths that "half the time […] were even marked with little arrows leading to gates to climb over."
The book is set an unknown number of years in the future. Modern technology like email and Internet are around, but nothing noticeably out of the ordinary like flying cars or teleportation gives us any hints that things might be far in the future. Could be two years from now, could be two hundred years from now—World War III's going on, but the Enemy is unnamed, giving us no further clue as to who might be fighting with England. It's something about "oil, money, land, sanctions, democracy" (2.3.16)—which obviously narrows the playing field a whole lot. Not.