So the effects of the Plague of Justinian on the eastern roman empire are pretty well discussed but do we know much about how much is spread and the effects of it over in western and norther Europe? I'd guess it'd spread more slowly out in places where the remains of the empire's trade network were less intact like Britain. Are there not enough written sources and I'd be better served to ask the archaeologist?
I (albeit very briefly) mentioned the possible impact of the plague on the demography in Early Medieval British Isles in this comment for the question, Why was the population of England lower in 10/11th Century compared to when the Roman Empire was there?
The written sources in the British Isles, the Briton-Irish ones (Annals of Ulster, Annales Cambriae) as well as Anglo-Saxon one (Bede) note several outbreaks of the plagues from the 6th to 8th century, and the earliest entry of such plague dates back to the end of the 540s: [Added]: 'The great death in which Maelgwn, king of Gwynedd died. ‡ Thus they say 'The long sleep of Maelgwn in the court of Rhos'. Then was the yellow plague' (Annales Cambriae, a. 547) .
Gregory of Tours also mentions contemporary plague outbreaks in Merovingian Gaul several times in his History of the Franks: Books I-X (Link to dated English translation), especially in 4.31 (ca. 570? in Clermont), 9.21-22 (ca. 588 in Marseille), and 10.1 (ca. 590 in Rome).
AFAIK there are some contemporary sources to record the outbreaks, but we don't have enough archaeological evidences to complement them and identify these entries with the bubonic plague. The high mortality of the disease, however, suggest they were indeed so.