It's never easy to admit that you have called it wrong. Before the launch of BBC1's Sherlock last month, I suggested that what the world didn't need right now was a new Sherlock Holmes adaptation, whereas, it seems, that is exactly what the world needed right now.

My point had been that when every modern fictional detective is basically derived from Sherlock Holmes, and CSI and its ilk have milked dry the science of forensics – Holmes's USP – updating Conan Doyle to the 21st century seemed a somewhat redundant exercise. That, however, was reckoning without the bold, inventive and witty minds of Steven Moffat and Mark Gatiss. Their loving trilogy of 90-minute dramas has rightly been the runaway TV hit of the summer – and made a star of an actor, who is, in Moffat's words, "the only man to play Sherlock Holmes with an even stupider name".

His name still doesn't trip off the tongue, but welcome to the TV stratosphere, Benedict Cumberbatch. Robert Downey Jr's reign as the hippest new Holmes on the Baker Street block has proved short-lived, and this BBC version should cast a long shadow over Guy Ritchie's movie sequel, especially as the Moffat-Gatiss version airs in the US in October, and will have plenty of time to embed itself in international viewers' consciousness before Ritchie's sleuth returns to cinemas at Christmas 2011.

"Sherlock fever" has even followed Cumberbatch to the National Theatre, where he has, until last night, been appearing in Terence Rattigan's After the Dance. Although the run was already sold out on the back of strong reviews, long queues for returns and day tickets began forming early in the morning once Sherlock started airing on BBC1. "We also picked up a lot Tweets in recent weeks about Cumberbatch being in the play," says a NT spokesperson. Indeed, Tweets, dedicated online forums and seemingly endless blogs have been littering the internet since the start of the series.

Cumberbatch's updated version of the fictional Victorian detective has even, apparently, become a fashion icon, as "Sherlock chic" (as it's already been dubbed) hits the catwalks and fashion stores. Savile Row tailors have reported a jump in enquiries from gentlemen keen to copy the extra-long tailored coats sported by the actor, Debenhams menswear has announced a surge in enquiries for similar coats, and designer Paul Costelloe has already stepped up to meet demand, offering tailored coats and scarves based on the series. And for the women? Sherlock, it seems, is well in tune with the sartorial zeitgeist. "Capes are going to be massive," says Emma Elwick, market editor of Vogue. "There is something elegant and dramatic in the swoosh of a cape."

The series has even been raised in the Commons, with coalition Culture Secretary Jeremy Hunt telling the House: "It was a very good example of the BBC at its best, investing in new programming." That's music to an embattled BBC's ears, and with such a wide cultural impact, not to mention the 7.3 million viewers who tuned into last Sunday's final episode (in which we finally met Holmes's nemesis Moriarty), it's hardly surprising then that the BBC plans to re-commission Sherlock. No official announcement has been made yet – timings and availability have still to be thrashed out, and all that – but Sherlock producer Sue Vertue and her husband, Steven Moffat, appeared on the BBC Breakfast sofa earlier this week to say the words that fans had been waiting for. "There will be more," announced Vertue. "We're having a meeting to talk about how many and when really."

So what went right? After all, as the BBC's head of drama, Ben Stephenson, recently admitted: "I thought Sherlock would be big because Steven is a god, Benedict and Martin [Freeman, who plays Dr Watson] are a fantastic pairing and the direction was brilliant. But you never know until you put it out." What seems more important than Moffat being a "god" is the fact that he is a "geek" – indeed, that he and Mark Gatiss are self-confessed "Sherlock Holmes geeks" who discussed their plans to bring the stories to the screen while travelling to and from Cardiff, where Doctor Who was being filmed (Gatiss also writes for that series). They love the books, in other words, and having, in anticipation of the first of the BBC episodes, A Study in Pink, recently myself read Arthur Conan Doyle's first Holmes story, A Study in Scarlet, it's easy to see where they have kept to the original, and where they have deviated from it.

Many parts didn't need updating. There were some groans, for example, when Cumberbatch's Holmes described himself as a "consulting detective", as if this was a clumsy attempt at modernity, but that, in fact, is how Holmes introduces himself in A Study in Scarlet. And Moffat-Gatiss also include an aspect of Holmes's intellect ignored by other screen versions: the fact that the great detective is completely clueless in some regards, that he wilfully ignores all aspects of "useless" knowledge – such as politics, philosophy and the fact that the earth revolves around the sun – that might otherwise clutter his mind.

Other clever updatings to 21st-century London have been much commented upon, including the on-screen text messages and web searches, the fact that Dr Watson writes a blog about Holmes's deeds, instead of a journal, and the nicotine patches instead of a pipe... ("this is a three-patch problem..."), but all would come to nought without the inspired casting of Cumberbatch and Freeman. "Benedict was the only person we actually saw for [the part of] Sherlock," said Sue Vertue. "Once Benedict was there it was really just making sure we got the chemistry for John – and I think you get it as soon as they come into the room, you can see that they work together."

Indeed, Cumbertach's somewhat Asperger's Holmes is beautifully complemented by Freeman, who gets plenty of opportunity to essay that bemused look perfected as Tim in The Office. An eccentric, other-worldly genius in a long coat and a bemused sidekick whisked away on extreme adventures – the similarity to Doctor Who is perhaps unsurprising given Steven Moffat's involvement – we even had the long-anticipated appearance of Moriarty, with echoes of the appearance of the Master in Doctor Who. Interestingly, Matt Smith, the current Timelord, and Cumberbatch were GQ's "Most Stylish Men of the Week" on consecutive weeks.

London looks stylish too – both contemporary and timeless. And the supporting roles have been cannily cast – from Una Stubbs as Mrs Hudson ("a nice murder – that'll cheer you up", she tells a morosely bored Holmes in last Sunday's The Great Game) to Gatiss himself as Holmes's older brother, Mycroft.