Probably one of the worst history books I've read. Unfortunately for Peter Reid, I have the breadth of experience to spot just how he manages to miss the mark. It's definitely not the worst piece of scholarship on the subject, but the manner and style of the prose fall flat.
As mentioned in his introduction, Peter Reid held the rank of Major General in the British Army, and I believe that reflects on the shortcomings of his book. Typically, a purely military history will have reams of numbers, troop movements, weather conditions, detailed maps, times, and all manner of orders given and assumptions made on the motivations and skills of the involved parties. In addition, a rigorous academic history will contain copious amounts of citations, references to pipe rolls, letters, census data, and all manner of contemporary commentary with citations to explain the context, give the original translation, and compare to other sources. On the other end of the spectrum, a more 'casual' history novel should be very engaging, emotive, and strive to draw in the reader with pithy comments, and promote and definitive and strong conclusion supported by sources.
The absurd amount of detail above is necessary, because "A Brief History of Medieval Warfare" attempts to be all three at once, reaching none of the potential of the individual types.
The most notable problem with this take on the English military is the lack of good maps and clear, coherent troop information when describing important battles. The maps themselves are woefully inadequate to convey any significant detail. Most importantly, there is a severe disjointed presentation to the various marches over France. Reid references towns and cities on the way, but lacks maps to explain to anyone not well-read in medieval French geography. While Reid does at some points detail the logistics and difficulties of war, such as supplying arrows, how many arrows are fired in how long etc, it never reaches the point of a cohesive military telling. I suppose 'Brief' is apt for this, but it doesn't forgive the confusing prose.
For a rather long history book, passages from primary sources are very seldom cited and explained. In addition no mention of particular chroniclers stood out as important, and quite often contemporary records were dismissed offhand as implausible without mentioning why. Clearly, it would not be practical to present the reams of data available, but at least the sources should be cited to support major arguments.
Overall, while full of many interesting details, such as how guns first became used in sieges, how baggage trains worked, and the details of the War of the Roses, I found myself constantly thinking of just how boring and uninteresting the material was. As someone who normally takes great interest in this subject, to be put off by the writing style and presentation is significant. I have been reading some exceptionally high quality books lately, so my perception is skewed, and I can admit that this book covers the subject material quite well, just not to the standard I'm accustomed.
As a final note, I know some authors try to inject a little humor or dry wit into their writings, but the frequent use of exclamation marks in several places seemed extremely out of place.