The headline news about Sherlock Holmes And The 12 Days Of Christmas is that it marks a rare new collaboration between Tim Rice and Andrew Lloyd Webber, 49 years since their last full musical together, Evita.

Their contribution to a silly detective spoof is surprising, unless you know that star and co-writer Humphrey Ker’s sister Clare is married to Sir Tim’s son Donald, who’s producing this show with his sister Eva. It’s a family connection he’d have been foolish not to exploit, even if the resultant musical numbers seem tagged on to the show, rather than inherent to it. 

The songwriting legends certainly sprinkle a bit of joy in the opening number Christmas Lights, celebrating the magic of theatre at wintertime which establishes that the murders the great Holmes is investigating all happen in London’s West End – but the other numbers are generally surplus to requirements. Another memorable song, Dr Watson’s ballad Houses Are Not Holmes, actually adds a maudlin quality that fights against the comedy a little. It’s symptomatic of a show that is never consistently sure what line to take, though there’s plenty of fun in its execution.

At its heart is the sort of mock melodrama that Ker and co-writer and co-star David Reed performed in their comedy troupe The Penny Dreadfuls, especially the historical epics they made for Radio 4. But they’ve felt the need to boost the subtle absurdity of the humour in those fond parodies to fill the big Birmingham rep stage.

Also added is some pantomime business, most of which comes from scene-stealing Cameron Johnson as the dame Arthur Stone, initially cracking some suitably cheesy puns before later becoming a potential victim of our serial killer, who is working his way through the 12 Days Of Christmas

The show’s wilfully labyrinthine plot sometimes works against it, with convoluted explanation and motive – and the unfollowable leaps of imagination Ker’s Holmes makes to solve the crimes – making the story difficult to invest in.

Add in other strands about Watson (Reed) feeling underappreciated by his demanding companion, and Holmes being threatened by an upstart new consultant detective who is – shock – a woman called Athena Faversham (Helena Wilson) and you’ve got plenty going on. These latter storylines actually hold the real engine of the show beyond all the noise of the murders, while the script is playful with its casual anachronisms, acknowledgment of its silliness, and fourth-wall breaking.

The performances are on point – especially Reed and Welcome To Wrexham star Ker, who hit the right balance between taking the mickey out of the Holmes genre while maintaining much affection for their character.

John Kearns is effective as Inspector Lestrade, a well-meaning but overwhelmed and stressed man well out of his depth being easily within the comedian’s wheelhouse, ensuring he slots neatly into the ensemble. Regular Penny Dreadfuls collaborator Margaret Cabourn-Smith is housekeeper  Mrs Hudson and - most memorably - an eavesdropping, plot-advancing crone.

Meanwhile another comedy name, Susan Harrison, brings suitable levels of chipper, chin-up enthusiasm to the plucky urchin Ernie who helps Holmes and is in her element in the jaunty musical numbers.

Of the Baker Street Irregulars who are Holmes’s ears and eyes on the street, Ker’s character deadpans that recruiting underage homeless helpers to do his bidding  is ‘perfectly normal’, one of many wry asides cheekily satirising both the era and clichés we’ve come to associate with Arthur Conan Doyle’s creation.

Such playfulness can sometimes be subsumed by the knotty whodunit – which doesn’t resolve artfully enough for genre fans, but prompts the melodramatic showdown which the storyline surely demands. 

The Victorian era is inherently Christmassy, and the traditional set adds to the festive feel – as, especially, does a song-and-dance number purportedly from the Royal Command Performance where the criminal capers reach their denouement. It’s all catnip for those who’ve grown out of panto but still want some light seasonal theatrical fare that this show provides.

• Sherlock Holmes And The 12 Days Of Christmas runs at the Birmingham Rep until January 18.