I would recommend: The Story of Britain: From the Romans to the Present: A Narrative History, by Rebecca Fraser. I found the book to be accessible, unpretentious, and a good survey of British history since Roman times. It was evenhanded and meritorious in its handling of more controversial moments in British history—Margaret Thatcher's time in leadership, for example. While it is close to 800 pages in length, it can be brief in covering events at times. Still, it makes for a wonderful introduction .

If you are truly dedicated to your quest—and you want something much more in-depth and scholarly—I would recommend the new Oxford History of England. It covers the history of England and later Britain in great breadth and detail, comprising eleven volumes to date (and more on the way.) Its sourcing is top-notch and its writing, while academic in quality, is quite readable to the lay-person. But it is not for the faint of heart, and it can be quite expensive.

Simon Schama narrated a nice documentary and wrote an accompanying book - A History of Britain. I recommend both.