There’s a passage in Vasily Grossman’s Life and Fate in which the author imagines the parallel lives of a man and his murderer. “If one man is fated to be killed by another,” he writes, “it would be interesting to trace the gradual convergence of their paths. At the start they might be miles away from one another … and yet eventually we are bound to meet, we can’t avoid it…” This is the idea that animates Robert Harris’s latest novel, Act of Oblivion, which, although it is set in the 17th century, sends the reader on a riotously enjoyable and thoroughly modern manhunt that weaves between Restoration-era London and the wilds of pre-revolutionary New England.

The 1660 Act of Oblivion of the title was the edict in the wake of the fall of the English Commonwealth that pardoned all those who took up arms against the king save those who had a direct hand in Charles I’s execution. Many of these so-called regicides are already dead – Cromwell himself had died two years prior to the Restoration in 1660. But one of the most prominent names on the decree that sealed Charles’s fate was that of Colonel Edward Whalley, a cousin and childhood friend of Cromwell who has fled to America with his son-in-law, another regicide, Colonel Will Goffe.

Act of Oblivion is a book rich in the illuminating details that bring the past to life. While the language is modern, the book is given texture by the friction of scratching wigs and rough leather boots; the wounds of the brutal civil war are still visible on men’s bodies and in the undercurrents of partisan feeling, which mean that, even in America, Whalley and Goffe cannot be sure of their reception. One of the things that gives this book such a ring of authenticity is that Harris has constructed his novel almost entirely from factual material. The words may be imagined, but the architecture of the plot and the identities of the vast majority of its characters are drawn from Harris’s extensive research.

The only figure he has invented is the warped and vengeful manhunter, Richard Nayler, who is driven by motives both personal and political to track down Whalley and Goffe. He carries with him a handkerchief dipped in the dead king’s blood. “The martyr’s blood had dried over the years to a faded rusty colour. Perhaps one day it would disappear. But as long as it existed, Nayler had vowed to do all in his power to avenge the events of that January day.” Nayler is part detective, part monster, causing others to ask: “What makes him run so hard?” The answer is a mixture of thwarted ambition, resentment, and above all the loss of Sarah, his great love, in the wake of his imprisonment by the Roundheads. It was Whalley and Goffe who ordered his arrest, and he will stop at nothing to track them down.

Meanwhile, we follow the turbulent paths of the fugitives in the Puritan communities of New England. Both have left families behind in England and their stories too are woven into the narrative, particularly that of Frances, Goffe’s wife. The men are not young – Whalley is in his 60s, Goffe in his early 40s – and the lives of fugitives are not easy. Goffe misses his young family, a link to England that he is unable to sever, a touching element of humanity that rounds out this otherwise stern figure.

One of the challenges of writing about this period is that the intricacies of religious faith and faction can seem distant and abstruse to a modern audience. Goffe is a religious man – he had wanted to become a minister before the war intervened – but Harris doesn’t allow himself to become hung up on the niceties of Christian doctrine. Rather, he makes a broader point about the position of the colonels in New England: the simplicity of their faith and anti-monarchical feeling finds a natural home among the dissenters and Puritans of the New World. The impulses that would animate the revolution a hundred years hence were all there in the English civil war. This does not, alas, mean that the men have an easy time of it in Massachusetts.

As Nayler arrives in America, the pace of the novel increases, the sense of an inevitable meeting propelling the narrative forward. The chapters, paragraphs, even the sentences become shorter as the colonels seek to evade their monomaniacal pursuer. As always with Harris, there’s a delicious sense of being in the hands of a master, of watching as the pieces of the narrative puzzle fall into place. Act of Oblivion is a fine novel about a divided nation, about invisible wounds that heal slower than visible ones. Like Ishiguro’s The Buried Giant, it feels like an important book for our particular historical moment, one that shows the power of forgiveness and the intolerable burden of long-held grudges.

• This article was amended on 30 August 2022. The Act of Oblivion was passed in 1660, not 1652 as an earlier version said.

• Act of Oblivion by Robert Harris is published by Cornerstone (£22). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply