Melvyn Bragg is the well-known writer, editor, and producer of the long running British South Bank Show, and is also a prolific writer and novelist. He is not a linguist, but with his background as a journalist for the BBC, he does appear to know how to collect and compile reasonably accurate information and make it presentable, readable, and accessible to anyone with a high school level education.
I suppose if someone wants an authoritative discourse on the development of English, there is always the Oxford History of English. However, a quick check on the Amazon site for that particular book shows exactly zero reader reviews, suggesting that it isn't exactly a best seller. I'm sure linguists consult books written at that level regularly, but for someone who wants a quick overview written in readable prose, Bragg's book is not bad.
I am not a historian by trade, though I am reasonably well-read on the subject. I did not detect any glaring historical errors in Bragg's book, though to read some of the one-star reviews you'd get the impression he completely fumbled the research. I don't believe that is the case - if there are mistakes here in the research - then they are minor and nothing that I could detect.
My chief complaint about the book is regarding Bragg's style. This is a book about the English language, so perhaps all the verbal flourishes were intended to highlight the utility of English to convey thoughts not only precisely but artistically. Nonetheless, I found the prose a bit much - a bit too flowery and florid and overdone. Writers are not supposed to call attention to themselves by overdoing the so-called fifty-dollar words - I think Bragg should have toned the descriptives down a tad. He also decided to personify the language - talking about the English language throughout the book as though it was some kind of living entity capable of making decisions and performing actions. When combined with the aforementioned flowery language, this became a distraction and really did not contribute to the book whatsoever.
That said, I learned a good deal of new information, so I think, all in all, this was a worthwhile read. I am not sure I will run out and read everything else Bragg has ever written, but he is to be congratulated here for producing a book on the history of the English language that should be accessible to the average high school or college graduate - which is in keeping with the spirit of his television program as well.