Religion has previously not figured prominently in Kathy Reichs’s novels, and the fact that her latest involves fanatical believers battling to stop secrets about Jesus emerging suggests that she is responding to the success of Dan Brown’s The Da Vinci Code. Largely set in Israel, Cross Bones (Heinemann £17.99) features two skeletons that might be Christ’s, a tomb that might be his family’s, plus clues that he could have been alive at the time of the siege of Masada in AD73 and that his followers fought there with other anti-Roman insurgents — discoveries that, if genuine, threaten several official versions of history. Brown’s protagonists face opposition only from Opus Dei; whereas Reichs’s forensic anthropologist Tempe Brennan (teamed up here with her cop boyfriend Andrew Ryan and an archeologist) works out that their mysterious enemies could be Christian, Jewish or even Muslim fundamentalists. Skilfully combining a murder mystery with her biblical themes, Reichs is on top form. Her writing has an extra energy, perhaps derived from the rivalry with Brown, perhaps from Jerusalem’s edgy atmosphere; and there’s a new confidence in handling scenes of physical danger,which have been the weakest elements in earlier works.

Robert Edric concludes his determinedly glum Hull trilogy with Swan Song (Transworld, £16.99), a whodunit concerning the brutal murders of four women, two of them prostitutes. Private detective Leo Rivers is hired by the mother of Paul Hendry, who is believed by the ambitious local police chief to have committed all four. Soon convinced Hendry is innocent, Rivers then has to establish — by interviewing relatives and friends of the victims, and collaborating with a cop from the national crime unit and a criminal profiler — whether there are links between the deaths pointing to a single perpetrator; and if so, who the real killer is. Although his plot unfolds convincingly, Edric (whose pre-trilogy works were literary novels) is stubbornly resistant to the other requirements of his adopted genre. Rivers is a mere cipher, and the stiff way the characters speak belongs in an England of 50 years ago.

The contrast with another literary author’s venture into detective fiction could hardly be more striking. City of Tiny Lights (Viking £15.99), by the 2001 Whitbread novel prizewinner Patrick Neate, introduces us to Tommy Akhtar, a London private eye devoted to whisky and cricket. Asked by a West Indian hooker to trace her missing Russian colleague, he gets caught up in an imbroglio also comprising the death of a junior government minister, and links between American and British spooks and terrorists who are ostensibly their arch-enemies. Eventually he himself is suspected of masterminding terrorism, after misguidedly asking a kid he knows (who is then sent out to blow himself up on the Tube) to infiltrate a fanatical group’s meetings. Resembling Zadie Smith’s White Teeth rewritten as a crime caper with a male Asian hero, the novel — full of snappy dialogue and zany secondary characters — has enormous charm, and its portrayal of London (harmonious haven for disparate refugees, or pre-apocalyptic Babel?) is absorbingly ambiguous.

Incendiary (Chatto £10.99) seems to be set in 2008 and takes the form of a long letter to Osama bin Laden by its unnamed female narrator. Robbed of her son and husband when they are among 1,000 people killed by suicide bombers at an Arsenal match, she appears to be recovering from this trauma when she gets a job working at Scotland Yard for a policeman involved in counter-terrorist operations, with whom she has an affair. But she has also become entangled in the lives of a pair of journalists who ruinously persuade her to tape her lover secretly. Chris Cleave’s debut is two different novels jammed together: a thrillerish yarn about a British 9/11, and a tale of manipulative toffs exploiting an innocent. Fusing them proves impossible, and the device of the Bin Laden letter comes across as a futile gimmick. You have to admire the bravado, however, of a male author who spends all his first novel inside a woman’s head.

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