Dawn Hadley's Vikings in England (2006) is probably your best bet for starters. I think it's a well balanced read and a good discussion of the evidence, and I like that Hadley keeps an optimistic tone about how much more we have yet to learn.

But since Hadley sometimes seems to offer more attention to what scholars have been doing in recent years than on what the actual people in the Viking Age were doing, it might be worthwhile getting into some more of the nitty gritty situations. In my opinion, nobody makes the Viking Age in England come to life quite like Robin Fleming in her Britain after Rome (2011). Fleming was writing for a series that expressly prohibited long discussions about scholarly debates, and she set herself the task of writing a history of Anglo-Saxon England (including some chapters on the Viking Age) primarily from archaeology. It's a pretty unique perspective.

Since you're getting into this kind of literature, I'm assuming that you already have a feel for the general outlines of Viking Age history. If not, I always recommend Peter Sawyer's Oxford Illustrated History of the Vikings (2001) as a good way to familiarize yourself with the things and events that scholars most frequently refer to, and I honestly think the pictures really help make the period feel a bit more real. For a more up-to-date and comprehensive survey, although perhaps a bit more awkward as an introduction to the Viking Age, there's also Stefan Brink and Neil Price's Viking World (2008).

Finally, there's a lot of articles that might also speak to your interests as well. I'd especially recommend Lesley Abrams' "Diaspora and Identity in the Viking Age," Early Medieval Europe (2012), as well as any of several articles by Clare Downham. I think "Viking Ethnicities" might be best, but "‘Hiberno-Norwegians’ and ‘Anglo-Danes’" might speak more immediately to your interests. (First two links go to academia.edu with pdfs online; third link goes directly to a pdf.)