At the very least, some of the Frisian dialects were very close to Old English of the Anglo-Saxons. With little written work surviving of some of the Germanic languages, the exact degree of comprehensibility is always going to be uncertain, but it seems clear that there was certainly some mutual ground.

Several stories of Anglo-Saxon clergy ending up in various Germanic-speaking parts of the continent imply there was some degree of mutual understanding: St. Wilfrid was able to speak to the local Frisians after being shipwrecked there, and there is no implication in the various Saints' Lives of the missionaries that they had difficulties communicating with the local people (compared to, say, the notes in Bede's Ecclesiastical History about King Oswald's noteworthy ability to speak Irish and how he acted as interpreter for Bishop Aidan).

Furthermore, there is an Old English poem, Genesis B, which is a translation of an Old Saxon poem on the same subject. Before the latter was discovered, Eduard Sievers postulated the existence of the Old Saxon Genesis based on the phrasing of some parts of Genesis B, suggesting the two languages were similar enough that instead of a complete translation, the Old English writer had retained a large degree of the Frisian style.

In short, they were almost certainly some degree of mutual comprehensible, though both sides probably had to concentrate during a conversation.

Sources: Breul, K., 'Eduard Sievers', The Modern Quarterly of Language and Literature Vol 1 (1898), pp. 173–175

Lapidge, M., Blair, J., Keynes, S. and Scragg, D. (eds.), The Blackwell Encyclopaedia of Anglo-Saxon England (Oxford, 2001)

McClure, J. and Collins, R. (eds.), Bede: The Ecclesiastical History of the English People, The Greater Chronicle, Bede’s Letter to Egbert (Oxford, 1999), p. 114

Webb, J. F. (trans.), 'Eddius Stephanus: Life of Wilfrid' in The Age of Bede (Harmondsworth, 1983), p. 132