Last Night's TV - Luther, BBC1; True Stories: Erasing David, More 4

Keep watching this detective

John Luther has just returned from a long period of gardening leave, while an internal investigation establishes how he – oops – failed to prevent a serial-killing paedophile from falling four storeys. His immediate boss – Saskia Reeves, 'eaving out 'er 'aitches to show how down to earth she is – would like him to play it by the book in future. He is, she tells him at the beginning of Neil Cross's new detective series, Luther, to "observe case management protocol... any proactive strategies to be signed off by me". Fat chance of that, we know at once, because the only book Luther appears to care about is "So You Want to Be a Maverick Detective". Rule One. Have relationship difficulties so you can gloom about the place in between pounding desks and chasing killers. Tick to that, since Luther has just discovered that his wife plans to make a temporary separation permanent. Rule Two. Combine a penetrating psychological intuition with a grasp of the basic rules of evidence that would shame a probationary constable. Tick to that too, since all it took for Luther to spot that his suspect was a "malignant narcissist" and had just topped her mum and dad was the fact that she didn't yawn after he did during an interrogation.

And yet, despite the fact that that was all he'd got to go on, he still threw a tantrum in his boss's office when she was eventually released. Rule Three. Be a lot brighter than any of your suspects expect you to be. Big tick to that, given that Luther is able to discourse suggestively about dark matter and Occam's razor in a way that sends a frisson of sexual thrill through the psycho-killer physicist he's trying to crack.

They're so conventional mavericks, these days, rarely enlivened by anything that would genuinely give the conventions a bit of a twist, such as a passion for Civil War re-enactment, say, or a happy home life with a drag queen. It's all lonely drinking in late-night pubs and revelations of existential angst: "I love to talk about nothing... it's the only thing I know anything about," Luther said at one point. But Cross's series does have some things going for it. One is Idris Elba, who was magnetically commanding as the Baltimore drug dealer Stringer Bell in The Wire, and makes a pretty good fist of the hand he's dealt here. You might suspect that Luther is more a loose constellation of cop-show clichés than a fully formed character, but Elba brings the clichés to life on more than one occasion, his eyes jittering from agitation to acceptance in a way that suggests that there really is something going on behind them. Another thing in its favour – though you'll have to suspend your disbelief to relish it – is the pathological flirtation between Luther and the killer he can't quite nail, which looks as if it will run through the series to deliver a bit of Hannibal Lecter intrigue. It is, there's no getting away from it, a bit of a comedown after The Wire. But then it's hard to think what wouldn't be.

The killer in Luther did a swift bit of Googling at one point, learning all she needs to know about his private life with a few quick keystrokes. All of his intimate connections and weak points are laid bare – a facet of contemporary life that was the starting point for David Bond's True Stories documentary, Erasing David. His idea was to play a 21st-century game of hide-and-seek. He would try and disappear and two private investigators would attempt to track him down, the purpose of the exercise being to reveal the tangled snare of inadvertent revelations that any modern transaction leaves behind it. And it was eminently watchable both for the fieldcraft of a contemporary manhunt – which ranges from sifting through your bins to triangulating the position of your last phone call – and its revelation of the submerged iceberg of information that lies beneath the surface. The film ran like a thriller, cutting between his attempt to stay invisible and the ingenious trawling of his chasers, and finding time as well for the thoughts of civil- liberties activists such as David Davies and Henry Porter.

Bond – and a lot of other people – worry that having the architecture of a police state in place make it a lot easier for a police state to occur. And it's true that we're sometimes blithely unquestioning about the uses to which our private information could be put, by someone who didn't have our interests at heart. But the final conclusion of Bond's film – he was caught after 18 days when he attended an ante-natal meeting with his wife – left several questions unaddressed. For example, what's the difference between privacy and loneliness?

Every human connection leaves a trace behind it – whether computer databases are involved or not – and sometimes an officious protection of individual privacy can be as onerous and soul-destroying as the alternative. Bond was caught because an NHS receptionist confirmed the time of his appointment to an investigator pretending to be him on the phone. His wife said she was shocked. But would she really want to live in society where, if you forget the time of your doctor's appointment, nobody will tell you what it is unless you supply a proof of address and a valid ID first? Trust is risky, but it's not always naive.