I am vastly interested in the subject, yet there is no mention of it in the book list, and I can't seem to find many books on it otherwise, much less their reliability and general readability.
If your 'the Anarchy in England' means the famous (notorious) civil war period in the 12th century, I can mainly recommend the following ones:
The historiographical topic of 'Anarchy' period almost inevitably intertwined with how we evaluate the various aspect of politics under the reign of King Stephen (1135-53). In short, the good book of 'the Anarchy' is the good book on him at the same time, and you have plenty of them. Among others, two collection of essays, respectively edited by Dalton & White and by King represent the development of the revisionist interpretation of Stephen's reign that had originally been initiated by Edmund King in the 1970s. King has been without doubt the leading scholar in this field of research, but if you find his writing style too heavy for your taste, I'd rather instead recommend Crouch's book as the first to read.
If you are not really confident on the essential knowledge of this topic, Carl Watkins' recent small booklet of Penguin Monarchs might also serve as an introductory work, though I assume that you have had enough knowledge of this period by reading some historical novels and TV series like Ken Follett's Pillar of the Earth or Ellis Peters' Brother Cadfael series.