The C-manuscript of the Anglo-Saxon Chronicle for 1039 notes:

'7 Wealas slogon Eadwine Leofrices bro?or eorles 7 ?urcil 7 ?lfget 7 swi?e fela godra manna mid heom' (Jebson, 1039).

Translation: And the Welsh killed Eadwine, brother of Earl Leofric, and Thurkil and Aelfgeat, and very many other good men with him (Swanton, 160).

This is thought to be the same conflict noted in the Breviate Chronicle:

Grifinus filius lewelin in norwallia regnare inchoauit qui dum regnauit anglos et gentiles persecutus est bellum in uado crucis super sabrinam cum eis commisit eosque deuicit (Gough-Cooper, b1060.1).

Translation: Gruffydd ap Llewelyn began his rule in North Wales, and he pursued the English and the Vikings (Gentiles) as long as he reigned. There was a battle at the ford of the Cross on the River Severn where he brought his men together and defeated them (the English) (Remfry, 173).

The Brutiau also note the battle and name the site as `Ryt y Groes? (Ford of the Cross) (Jones, 12), a name also given in the tale of the Dream of Rhonabwy (Richards, 37-8). A site in the vicinity of Buttington near Welshpool (SJ 246 088) has been widely accepted as the location of the battle and seems a suitable place for a battle on the River Severn, between the forces of North Wales and Mercia (Charles-Edwards, 562).

RCAHMW (Battlefields Inventory), Dec 2016

Bibliography
Charles-Edwards, T. M., Wales and the Britons 350?1064 (Oxford University Press, 2013).
Jebson, Tony, Manuscript C: Cotton Tiberius C.i: The Anglo-Saxon Chronicle: An Electronic Edition (Vol 3) online edition.
Jones, Thomas (ed. and trans), Brut y Tywysogyon or the Chronicle of the Princes: Red Book of Hergest Version (Cardiff, University of Wales Press, 1955).
Remfry, Paul M. Annales Cambriae: A Translation of Harleian 3859: PRO E. 164/1: Cottonian Domitian, A1: Exeter Cathedral Library MS.3514 and MS Exchequer DB Neath, PRO E. 164/1 (Castle Studies Research, 2007).
Richards, Melville (ed.), Breudwyt Ronabwy (Gwasg Prifysgol Cymru, Caerdydd, 1948).
Swanton, Michael, (trans. and ed.) The Anglo-Saxon Chronicle (J. M. Dent, London, 1996).