Within seconds of his first appearance as Captain Jack in Torchwood (BBC One, Thursday, 9pm), John Barrowman was showing off what he can do.

He can stand moodily in a cloud of steam. He can point a gun into the air for no apparent reason. He can run across a room without flapping his arms excitedly. The only skill of his that wasn’t on show was his greatest – his jazz hands – although maybe later in the series he’ll use those to startle an alien who’s never seen Me And My Girl.

It’s all this silliness that has always made Barrowman’s character a tricky one – essentially a nice idea that has never quite worked despite all the tuning the show’s creator Russell T Davies has done since the disaster of the first series of Torchwood (although he certainly deserves credit for being the first to introduce a bisexual character to a mainstream action show).

Even now, the problem is how to get the tone right. This is supposed to be the big brother of Doctor Who (the big brother who knows a few dirty words) but in the early days it felt like a family show that was trying to be rude and sexy for no good reason. Nobody was impressed. Nobody thought it was grown-up or clever. It was just showing off. Torchwood: go to your room.

To be fair, Davies sorted most of this problem by trimming off the extreme edges – but now, with this series, which is financed by the US network Starz, he’s faced with a new problem: how to make a British show that works in America but still works in Britain. Davies tries to solve this by having two strands – one in America, one in the UK – and by introducing new characters gradually. The best of these was Oswald Danes, a killer played with halting strangeness by Bill Pullman; the worst was Esther Drummond, played by Alexa Havins in the manner of a women presenting an infomercial on eyebrow pencils.

The central concept of the plot was fascinating too (what would happen if one day nobody died?) and as usual Davies delivers some moments you know are going to stay scribbled on the inner layers of your brain – in the first episode, it is the corpse on the slab that will not die. It was also a good opportunity for the British actors in the cast to show off their hospital acting. Every British actor can do it because every British actor has been in Casualty.

However hard Davies tries though, there always seems to be a chill in the middle of Torchwood, a coldness. Perhaps that’s because Davies seems to limit himself to one joke per episode (which is a pity because he’s good at jokes). Perhaps it’s because there’s still uncertainty about whether this is an adult show that’s been softened or a children’s show that’s been hardened.

In the end though, it’s probably because – unlike Doctor Who and Star Trek and all the truly great science-fiction series – there doesn’t seem to be a guiding philosophy at the centre of the show, a passion pumping life into it, a reason for being. Captain Jack may run around shooting people and punching people and occasionally snogging people, but if we stopped him and asked him why he was doing it, I’m not sure he’d be able to say. I’m not sure I can either.