Two solid recommendations:

• Robin Fleming, Britain after Rome: The Fall and Rise, 400-700 (London: Penguin, 2010), 366pp., $14. Fleming rejects writing history from the few details texts give us about early English kings. She tries instead to reconstruct the history of communities in Britain from the massive amounts of material evidence, which paint a very different picture. There are no footnotes, but don't be fooled: This is very serious history, and Fleming doesn't shirk from making important historical arguments. She has an ability to present archaeological evidence in a lucid prose that other historians would do well to emulate (e.g. pp. 18-19 on Poundbury cemetery; her concluding pp. 365-66). The subject and chapter bibliographies at the end are a rich resource for scholars and arm-chair historians alike. If you want to know what life was like in early medieval Britain, this is your book.

• Guy Halsall, Worlds of Arthur: Facts and Fictions of the Dark Ages (Oxford: Oxford University Press, 2013), 307pp., $20. Halsall likewise rejects the standard king-centric narratives, but he remains interested in how the kingdoms that show up in the 700s came into being. He begins with an important section on how early medieval historians figure out what our source texts actually mean, debunking some Arthur myths along the way. And he concludes with an entirely revised narrative (that not all historians will accept, but which is definitely thought-provoking), based largely on archaeology and comparing what was happening in England to what was going on elsewhere. Again, footnotes are absent, but there is a section on further reading. If you've got some background in interpreting primary sources, or if you're unsure what archaeology can add to the discussion, there's a lot to think about here. If you want to know how kings became so important, both in the course of actual historical events and more recently in our own writings about medieval history, Halsall will let you know.

I'm less certain about late medieval England, but one place to start looking is the Penguin History of England. Fleming's book is the second in this series. The other medieval histories sound more dynastic than you'd like, but if you can find them in a bookstore, they're both by excellent scholars, well worth a look in their own right, and should also have recommended reading sections that will point you on your way.

• David Carpenter, The Struggle for Mastery: Britain 1066-1314.
• Miri Rubin, The Hollow Crown: Britain 1272-1485.

there's a suggested reading list in the askhistorians wiki you might find useful.