I hope this question is specific enough for the sub-reddit's standards.
To give some background info that might help you tailor your response, I should mention that I am a graduating English/Early Modern Studies major that will be undertaking a Masters degree at Oxford University this fall. As a student of literature, I have a decent grasp of medieval history, but I'm far from being an historian. In light of this, I'm hoping to hit the books over the summer to help mitigate this historical blindspot and prepare myself for reading medieval literature at the graduate level.
I'm asking this question in /r/Askhistorians because it is deceptively complex. Good academic sources are usually quite narrow in focus, and larger overviews can be either poor in quality or incredibly long. As someone looking to finish this book over the summer, I am thus looking for a good balance of quality, historical depth, and page length. And because I will be using this knowledge to assist me in my graduate studies, I'd prefer that the book be academically credible (at least as an entry point into further research, anyway).
Thank you for any recommendations you can offer. Bonus points will be given for books that are easy to read for historically-inclined but non-expert individuals!
A professor of mine who specializes in medieval Britain had us read "The Anglo-Saxon Age: a Very Short Introduction" by John Blair. It is not kidding about being very short--seriously, this thing is a breeze to get through. They have other short introductions in the series that would absolutely help give you a good grasp on medieval Britain. This collection also has introductions to Roman and Medieval Britain that I would highly recommend. I also really enjoyed "From the Vikings to the Normans" by Wendy Davies. It only covers 800-1100 CE, but I think it would be a good start for you. Hope this helps you get started!
The Blair "Anglo-Saxon Age: A Very Short Introduction" recommended by /u/michellesabrina is good and short (maybe 100 very small pages with lots of pictures). You can read it in an afternoon easily. If you know nothing at all of the period, start with that.
But for your needs as an entering masters student, I think a better suggestion would be Fleming's "Britain after Rome." It's aimed at an educated reader, but not necessarily someone with any background in the period. It emphasizes archaeology over texts and so it will be a great corrective to the bias that you naturally get from studying literary texts. It's very readable and contains very current scholarship, but is broad enough not to get too bogged down in the kind of narrow focus you want to avoid.
Sorry I don't have anything similar to offer for the post-Conquest period.
A Brief History of Life in the Middle Ages by Martyn Whittock may be worth looking into. It only deals with the history of England and basically does not cover the rest of the British isles in any detail, and from what I remember (I don't have the book with me at the moment and it's a while since I read it) it doesn't have much stuff about the first few hundred years you're interested in (it covers the period 900-1553). But aside from that it seems to me like the sort of book you may be looking for. You can read my review of the book here.