On one hand, there's no reason at all for a new biography of Richard III, who ruled England for just two years and died facing the future Henry VII at the Battle of Bosworth on August 22, 1485. Certainly the discovery of his body under a car park in Leicester in 2012 added some gruesomely specific forensic detail to the story of his final moments. But otherwise it only confirmed what Shakespeare has already told us: that Richard III had a physical deformity, in this case a curvature of the spine caused by a medical condition called scoliosis.

On the other hand – and this is obviously the one publishers use to estimate sales – there's every reason. The global headlines which followed the discovery of the body, the high-level spat that erupted over where his remains should be re-buried, and Channel 4's decision to broadcast the ceremony all point to a single unassailable fact: we're still fascinated by the man portrayed by posterity as a homicidal hunchback and by generations of pro-Ricardians as a complex and pious king whose ruthlessness resulted from the political realities of the day. Readers love a good riddle, and by any yardstick Richard III delivers.

David Horspool, history editor of the Times Literary Supplement when he's not up to his eyes in medieval chroniclers, makes great play of his equanimity, though if I had to guess I'd say he has a deal of sympathy for his subject. But like any historian, he asks us to step away from the myths and the popular conceptions and examine the facts and the wider context. The question isn't whether Richard was pragmatist or sociopath, but the extent to which his world required him to be both.

Accordingly there are points at which every other page in Horspool's learned and entertaining read seems to feature an execution or murder. Though the main players are mostly titled and can be assumed to have at least paid lip service to medieval ideas of chivalry and honour, their antics read like gangsterism, pure and simple.

Look at Richard's role models. His paternal grandfather was beheaded for treason, and his second oldest brother Edmund died in battle alongside their endlessly belligerent father, Richard Plantagenet, Duke of York, who subsequently had his head placed on a spike. Richard was eight when all this happened. Born on October 2, 1452, he was child number 12 of 13, and Edmund wasn't the only brother who would meet a bloody end.

Horspool sketches in Richard's childhood and early adolescence as best he can (he's virtually invisible until his late teens) but offers a vigorous and vivid account of the milieu in which he lived, particularly Henry VI's disastrous reign and Richard's family's part in the the endless machinations of the competing power blocs. He gives proper time and consideration as well to both Richard's strengths as a military commander and his knack for acquiring property, land and friends (though not enough of the last, as it turned out).

As for the big question – did he kill the so-called Princes in the Tower? – Horspool answers yes, probably. The sons of Richard's dead brother, Edward IV, they should have expected their uncle's support. Instead, he usurped the throne intended for Edward V, the older boy, just days before the date set for the coronation. Here, Horspool's narrative sparkles as events unfold at blistering pace and Richard acts quickly to seize power and make a case for his legitimacy. And why did he do it? A mixture of pragmatism, greed, opportunism and impulsiveness, attributes common to any 15th-century noble but particularly one with a family history like his.

In his introduction, Horspool implicitly criticises previous biographers for failing to situate Richard within the wider context of European politics, the assumption being that he will do so. He also suggests that the period he covers is one with resonance for future eras. Richard, he writes, “lived through and fashioned pivotal moments in British history” while the Wars of the Roses, he thinks, are still being fought today.

I can't say he falls down on the first point. His narrative switches regularly between England, France, Burgundy and the Low Countries to show how continental dynastic squabbles affected the balance of power among the English nobility. And he's correct when he writes that the Wars of the Roses should be viewed as being about “issues of fundamental competence and the breakdown of the body politic” rather than “dynastic power games”. But if he's aiming for a thesis in which the Wars of the Roses can be viewed as leaving as heavy an imprint on modern Britain as, say, the Reformation or the Civil War, then he fails to make his case.

No matter. The conclusions Horspool nudges the reader towards – such as the presence of musket balls on the field at Bosworth meaning it was far from “the last medieval” battle, as it's sometimes portrayed, or that it was in this period of political cynicism that important seeds of social and political dissent were sown – do at least take the story forwards. His is an elegant and concise review of a period of British history that will fascinate us for some years yet. Now if only those bones could talk.