Egil Skallagrimsson (910-990), the Icelandic warrior-poet in King Athelstan's service, stated in his saga that the English marched up a long slope and formed on the long ridge of the hill with a river to their right (r.Rother?) and a dense wood to their left (Tinsley forest?), with a fort (old Roman- Templeborough?) on top ('Weondun'[holy hill] as northerners later stated).
This fort was probably one of the old roman frontier forts along what was the southern edge of Northumbria on the border with Northern Mercia, where King Edward 'the Elder' had built frontier forts decades earlier?
In front the land sloped away towards a distant town. Could this ridge/battle-site have been Brinsworth (Rotherham)? 'worth' and 'burh' are OE so Brinsburh could be Brunan-burh.
Michael Wood, in his book 'In Search of England', (and 1981 TV series “In Search of the Dark Ages”) makes the case for Brinsworth/Catcliffe, between Sheffield & Rotherham, south of the confluence between the rivers Don and Rother (the latter snakes around White Hill), where there was a huge, strategic old Roman fort (one of many in this region [built by Ath’s father] during a “dark age Vietnam” as Wood says) on the top of White Hill near the old Roman road, called Brynesford in the DD Book of 1086.
In Anglo-Saxon times it was called Brunesfort- the personal name of Brunan Burh, as Wood says.
Local Sheffield/Rotherham legend mentions a 'Scots army' that camped on Templeborough (an old local Roman fort);-
"...In the third part of ‘In Search of England’, Wood writes about places that illuminate interesting aspects of early England: Tinsley Wood, near Sheffield, which has been claimed as the site of Athelstan's great victory against the Celts in 937…”
AH Burne also suggests the mid-'England' site, near Sheffield, as the most likely Brunanburh battle-site. Assuming the alliance was to capture London, the old Roman 'great north road' (today's great A1 road) of eastern Britain from York would be a natural path, then as now.
The lie of the land here also fits perfectly with Sturlasson’s geographical description (fought down a hill, with forest and river on either side). Two transverse roads, the Via Devana and Watling Street, would have allowed Athelstan to block Olaf whichever route he took south.
This is A.P.Smyth’s suggested site for the battle – the Northamptonshire/Huntingdonshire border.
There is a forest (called Bruneswald) and between rivers Nene and Ouse.