I know there's nothing stoney to see here any more (the 'Keys to the Past' site says they were all gone by 1825). But it was such an impressive sounding thing. There's a lot of water merging and joining the North Tyne very nearby and you can't help but wonder if there's some relevance in that. In fact the following makes it sound as though the stones were very near to the water.
[Nunwick Hall] stands on a rising plain, which to the east has the appearance of a park [..] Two brooks unite their loquacious streams to give beauty and ornament to a neat garden [..] and thence take their course by another grove, on a declining hill, to the south front of the house, and fall two or three fields below into the river of North Tyne.
In an adjoining field, called, Nunswick-east-field, were five upright stone-pillars, in a circular order; four of them perfect and entire in 1714, the other broken; the perfect ones eight feet high, and nine feet and an half over; the circumference of the area in which they stood, ninety feet. Mention is made of them by Bishop Gibson in his Camden. In such kind of cirques, the Britons held their public assemblies, both civil and religious.
I looked up what Gibson had to say:"The huge heaps of small Cobbles are not the only Monuments which these Wasts afford. There are also large stones erected at several places, in remembrance (as is fancied) of so many battels or skirmishes; either anciently betwixt the Britains and Picts, or (of later times) betwixt the English and Scots. Particularly, near Ninwick, in the Parish of Simondburn, four such stand still erected; and a fifth lyes fall'n to the ground." (p870)