Sherlock, BBC One

There was a risk that this new take on the indestructible sleuth of Baker Street might be smothered at birth by a dust-storm of pre-publicity, with coverage stretching from the tabloids to Andrew Marr (who really seems to believe he's an arts correspondent, and not just Alfred E Neuman's long-lost twin brother).

But after being dropped into the midst of a claustrophobic and menacing-looking contemporary London, Holmes emerged as triumphantly his own man despite being deprived of deerstalker, violin, hansom cabs or Meerschaum pipe. The period update was cunningly managed. 221b Baker Street had progressed steadily downmarket, and was now a shabby flat above Speedy's Sandwich Bar & Cafe, thoughtlessly stuffed with Holmes's bric-a-brac and chirpily supervised by landlady Mrs Hudson (Una Stubbs).

The original Holmes was a compulsive sender of cables, but Cumberbatch's Doyen of Detection is an inveterate texter and internet-user, even if he has not yet conquered the commanding heights of Twitter and Facebook. To avoid having to show fiddly little shots of telephone screens, director Paul McGuigan had hit on the notion of converting texts into floating surtitles, branching out into explanatory on-screen notes during scenes where the Great Detective was poring over corpses for clues.

We were introduced to Dr Watson (played with compelling edginess and grit by Martin Freeman), a former army doctor trying to cope with post-traumatic stress and injury after a spell in Afghanistan, where, serendipitously, Arthur Conan Doyle's Watson had served in an earlier ill-judged military intervention. He was told by his shrink that writing a blog would be excellent therapy, and the blog replaces Watson's original diaries as the record of Holmes's new adventures.

The more you watched it, the more this present-day Holmes made sense. It even began to seem overdue, since the mythology and methodology of Holmes already resonate through a number of other popular TV shows. CSI's Gil Grissom is a Conan Doyle aficionado whose scientific and analytical approach to evidence-gathering is rooted in the Sherlockian tradition, and one CSI episode concerned a Sherlock Holmes society in Las Vegas.

Dr Gregory House carries that Holmesian adage, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth", to its icily logical conclusion, and it is no coincidence that he has a pal called Dr Wilson for good measure. Cumberbatch, who convinces you that he's operating at greater velocity and higher altitude than anyone around him, brings a glimmer of House to his Holmes.

Moffat and Gatiss had done their research, and they snapped up their Holmes-esque tricks with aplomb. Where the traditional tobacco-stained Sherlock would assess a complex case as "a three-pipe problem", Cumberbatch cogitated after plastering his forearm with three nicotine patches instead. The creators have speeded up his analytical insights to a frenetic, hilarious degree, enabling him to analyse Watson's life story, family relationships and present circumstances within seconds of meeting him. "What is it like in your funny little brains?" he demanded, horrified at the stupidity of all around him. "It must be so boring."

In a sly nod to the management-speak which disfigures the discourse of our era, Holmes is now a "consulting detective", running rings round the regular law-enforcement community. The police, headed as ever by Inspector Lestrade (Rupert Graves, permanently lagging two steps behind), are merely the groundlings in the theatre of Holmes's mercurial powers. "Shut up," Holmes snapped at Lestrade. "I didn't say anything," protested the Inspector. "You were thinking," said Holmes. "It's annoying."

Jokes aside, Moffat and Gatiss have dared to delve into the weirdness of Holmes, speculating about the psychological make-up of a man who's wildly turned on by the prospect of hunting a serial killer who forces his victims to commit suicide. The cops call him "Freak", and they warn Watson to stay away from him. But while Holmes, a self-confessed "high-functioning sociopath", and the damaged and lonely Watson barely know each other, they understand each other instinctively. Although they're not, as Mrs Hudson cheerfully suggests, gay.

This new-look Holmes started off as a 60-minute pilot, but the BBC liked it so much they commissioned three 90-minute programmes instead. Good call, because it's shaping up to be one of the TV drama events of the year.