Books I have enjoyed reading
Follies and Fallacies of Medicine  is my first recommendation, as an excellent and at times light hearted introduction to critical reading of articles about anything medical. I can do no better than quote from the introduction:
“The aim of our book is to reach inquisitive minds, particular those who are still young and uncorrupted by dogma. We offer no solutions to the problems we raise because we do not pretend to know of any. Both of us have been thought to suffer from scepticaemia* but are happy to regard this affliction, paradoxically, as a health promoting state. Should we succeed in infecting others we will be well content.
(*Scepticaemia: An uncommon generalised disorder of low infectivity. Medical school education is likely to confer life-long immunity.)”
Another excellent book is Hippocratic Oaths  by Raymond Tallis. This is a more heavy-weight look at medical care in the modern world. It is built on keen observation of the society in which we live, and certainly rings true to me in the description of the place of evidence in the misinformation surrounding MMR vaccination (amongst many other things). I found this one was best read in short bursts on the train.
Principles of Statistics in Medicine  by Bradford Hill is a clearly explained foundational text that opens up the basic principles of statistics used in medical research. My 3rd edition copy is inherited from my father when he was at Bart’s in 1946, but I see from the web that second hand copies of this early classic are still available. Otherwise you may find a copy in the medical library.
For the more adventurous reader I would recommend Dicing with Death  by Stephen Senn to stretch the mind into new areas of understanding. Not for the faint hearted.
 Tallis R. Hippocratic Oaths. London: Atlantic Books 2004.
 Bradford Hill A. Principles of Medical Statistics. Third ed. London: The Lancet Limited 1946.
 Senn S. Dicing with Death. Cambridge: Cambridge University Press 2003.