The D-manuscript of the Anglo-Saxon Chronicle for the year 1056, notes:

Se forlet his crisman 7 his rode 7 his gastlican w?pnu, 7 feng to his spere 7 to his swurde, 7 swa for to ferde ongean Griffin ?one Wyliscan cining, 7 he wear? ?'r ofslagen, 7 his preostes mid him, 7 ?lfno? scirgerefa, 7 manega o're gode men. ?is w's ehtan nihte 'r middansumere (Jebson, 1056).

Translation: He [Leofgar, Bishop of Hereford] abandoned his chrism and his cross, and his spiritual weapons, and took up his spear and his sword, and went thus to the campaign against Gruffydd, the Welsh king, and there he was killed and his priests with him, and the sheriff Aelfnoth, and many other good men, and others fled away. This was eight years before midsummer (Swanton, 187).

The Chronicle of John of Worcester adds that these events took place at `Clastbyrig? identified as Glasbury (SO 176 392) on the River Wye (Darlington and McGurk, 581). However, the Welsh chronicle O Oes Gwrtheryn also notes the battle, but under a different name.

O weith Machawy,hyd pan las Grufut ab Llywelyn pen orfu Ruffudd ab Llewelyn, ac y llas Esgob y Saeson (Jones, 4xx)

Translation: the battle of Machawy, when Gruffudd, the son of Llywelyn was victorious, and the bishop of the English was slain (Jones, 417)

Machwy has been identified with the river (named `Bach Howey? on historic Ordnance Survey mapping and `Bachawy? on modern mapping) which joins the Wye just to the east of the village of Erwood (SO 106 428), 7km north of Glasbury The battle possibly ranged between the two areas and the two sides have named it after the location most relevant to their view of the battle. Nothing more is known.

RCAHMW (Battlefields Inventory), Dec 2016

Bibliography
Darlington, R. R. and McGurk, P. (eds) and Bray, Jennifer (trans.) The chronicle of John of Worcester Vol. 2, the annals from 450 to 1066 (Clarendon Press, Oxford, 1995).
Jebson, Tony, Manuscript D: Cotton Tiberius B.iv: The Anglo-Saxon Chronicle: An Electronic Edition (Vol 4) online edition.
Jones, Owain Wyn, Historical writing in Medieval Wales (PhD thesis, Bangor University, 2013).
Swanton, Michael, (trans. and ed.) The Anglo-Saxon Chronicle (J. M. Dent, London, 1996).