They're creepy and they're kooky, mysteriously spooky and they have finally pitched up in the UK and Ireland for one big tour. Charles Addams' original characters were first invented as a nameless newspaper comic strip in 1938, since then his darkly weird, death-obsessed American family has featured in a TV sit-com, a hit film and a cartoon. The next step was, of course, a musical.

Andrew Lippa, Marshall Brickman and Rick Elice's show originally opened on Broadway in 2010 and it satisfied the legions of Addams Family fans out there (the show took £4.3 Million in its first five weeks), but not the critics. This production, directed by Matthew White, may be destined to do the same. While the performances and characterisations are great, the songs and plotting are less so.

The piece picks up at family crisis point, where Wednesday Addams – the macabre, crossbow-wielding daughter of Morticia and Gomez – has inexplicably fallen for the most jock guy you could imagine. We see nothing of their courtship, only that he has secretly proposed and his exceptionally straight parents are visiting for dinner from Ohio. Wednesday pleads with her family to try to be normal. She gets anything but.

The opening number's choreography – from Alistair David – is a lot of fun: a big set piece, with echoes of Michael Jackson's '"Thriller'" music video. But mostly the first half sets up the characters and deals with a fair amount of exposition and it drags. The humour within the piece occasionally feels a little weak, relying too heavily on the double takes and physical comedy from the cast. Oddly enough for a comedy, the script needs a few more one-liners. Grandma's "stay out of my s**t else I'll rip your leg off and bury it in the garden" line has the audience guffawing. But those moments are too few. It's not until the second half, where everything in the first half begins to get resolved, that the book and songs get snappier.

Overall, however, the songs are woefully forgettable, which is a big disappointment when you've got this crack cast delivering them. Samantha Womack's Morticia is the standout event of the evening. She has the character's sly smile, high cheekbones, and floating walk perfectly and she delivers her songs with verve, fringing everything with a smart wit. But it's hard to fault the rest of the cast too. Cameron Blakely as Gomez has a vast amount to do and he manages the comedy with the songs very well. Carrie Hope Fletcher as Wednesday is superb and her duet "Crazier Than You" - sung with her boy Lucas (Oliver Ormson) - is one of the most enjoyable in the show.

Elsewhere, rather surprisingly, Les Dennis may have found the part he was made for in Uncle Fester, the broad-shouldered bald-headed goon of an uncle, who acts as a kind of narrator. His squeaky broken voice is very funny and his timing and American accent is spot on. It's spooky how suited he is to Fester.

Diego Pitarch's high-walled creaky house designs smack a little of panto, and though his costumes work very well, they have a Phantom of the Opera ring to them. The nicest bits visually are the ensemble numbers – and here David's choreography helps no end.

Essentially the show veers jerkily, a little like Dickon Gough's Lurch, from the morbidly funny to the schmaltzy and too often the balance is off. Though The Addams Family isn't the nail in the coffin of theatre, it won't have you gleefully cackling at its ghoulishness either.

The Addams Family runs at New Wimbledon Theatre until 20 May and then tours the UK.

Click here to book tickets

Watch Carrie Hope Fletcher and Oliver Ormson in rehearsals