Industrial archaeology
They're not hi-vis waymarkers for obscure public footpaths through the countryside (though that wouldn't be an unreasonable guess of their purpose), they're actually the improbable relics of industry: coal mining. Most British coal was obtained from deep mining so that, while some surface evidence of the activity was visible and decidedly ugly, most was invisible beneath hundreds of square miles of significantly less ugly—indeed very attractive—cultivated countryside.
Even into the 1960s (unlike the USA) car ownership in the UK was not widespread. Until then—and certainly beforehand—it was common for coal miners to walk to work, sometimes over many miles. These white stiles were the waymarkers and access for those colliers traversing farmland to reach the pits at which they worked. It was (and may still be) possible to visibly track the path to the now-long-gone pits over acre after acre.
The white dot at the far end of the field in the photograph is the next stile on this route:
Before post-war nationalisation, much of the mining in this neighbourhood would have been in the ownership of the local Earl and his estate. Since the estate also owned the farmland over which miners walked, there would have been no opposition to the stiles and the access.
My grandfathers and two uncles made their living as miners. It was still a strong industry when I was small and the evidence of its presence—albeit limited and localised—was visible, despite the otherwise attractive aspect of the environment. One (now removed) example of this evidence protruded, in solitude, from a field close to my grandparents' rural home. It was both compelling to me as a child, and terrifying. It consisted of a concrete half-dome, about 10-15 feet in radius, bisected from apex to base to leave an open face that was closed by a large, barred, rusting iron gate, which was chained and padlocked. Clearly visible behind the bars of the gate was a chasm: immediately inside, the ground fell away at an alarmingly steep angle, a rail track at one side, a concrete stairway adjacent to it. They dropped quickly into darkness but not into silence: the sound of water—dripping, running, cascading—was constant, even in dry weather. Its actual purpose was an escape route from the mine far below, in the event of any subterranean catastrophe. To me it was like the frightful entrance to Hades. All the same, when we were walking my grandfather's dog along Spoutwell Lane, my brother and I would usually stop off in the field to scare ourselves anew.
Part of Roaming South Yorkshire.