A plausible re-assessment of the campaign, based upon what we know from the sources, is that there was possibly two invasions in 937.
Not later than August, Constantine of Scotland and Owain of British Strathclyde, possibly accompanied by Anlaf Sihtricson, struck into northern Northumbria, raiding extensively before moving to rendezvous with Anlaf G’s fleet on its arrival in September?
It is reasonable to assume that Athelstan responded by summoning his West Saxon and Mercian contingents, (Athelstan also hired mercenaries, incl. the Icelandic Viking Egil Skallagrimsson and 300 men with him) perhaps to Winchester and Nottingham as in 934, before marching north with this huge army to meet the invaders.
At news of Athelstan’s approach the coalition might reasonably in military strategy, have retreated further north to 'their lands' (the Danelaw side of the Mercia-Northumbrian border?), the adoption of some such defensive strategy being implicit in the OE poem and in the Latin poem’s account of the reaction to Athelstan’s approach:
‘The report of their conspicuous approach terrified the thieves, this clamour so shook the plundering legions, that, abandoning their spoils, they sought their own lands’