You may not know it yet, but mankind is at a critical time, a tipping point in the development of science and technology, a moment where we will all have to accept that human cloning must happen, mainly so David Tennant can be in everything.

Perhaps we have reached this point already. Flicking through the TV channels is like flicking through a scrapbook kept by one of his stalkers – all you can see is his face over and over again, with occasional breaks for the news. Many people embrace this, particularly those who loved Broadchurch. Others think: give another guy a chance.

Then you sit down and watch Tennant and you think: he is good, isn't he? In The Politician's Husband (BBC One, Thursday, 9pm), he plays MP Aiden Hoynes whose career is sliding while his wife Freya's (Emily Watson) is rising, and the frustration and anger in him looks genuine. At times, it feels like you can see right through his skin to the blood in his veins. There is never an artificial note, never a jump from one groove to the next. It's real. This is despite the fact the overall feel of The Politician's Husband is distinctly unreal at times. In many ways, it is like a forgotten Shakespeare play in modern dress. At one point, writer Paula Milne even gives Hoynes Shylock's words: "Villainy you teach me I will execute but I will better your instructions", although this only serves to show up how rubbish some of the other lines are. "To stay top dog," Hoynes says to his wife in the next breath, "you may have to unleash the bitch within you."

At times the plotting is Shakespearean too: confusing, labyrinthine, unlikely. For instance, Hoynes seeks to put his wife into the Cabinet as an agent of his revenge but never at any point does it feel likely. And revenge now is so boring anyway compared to Shakespeare's day. No one sorts things out with a rapier or poison in the ear. They do it by text message.

What is clear throughout – sometimes a little too clear – is that Milne has done her research. At times, you can almost see which political biographies she was reading before she sat down to write, but she certainly grasps at some lessons every politician should learn. Such as: politics is about the moment and realising it is the moment. Hoynes thinks he understands that, but gets it wrong. So did Michael Portillo, Michael Heseltine and David Miliband. For all those men, suddenly the moment was on the other side of a high wall, unreachable.

Even more interesting is what The Politician's Husband has to say about friendship. Hoynes thinks he is on the verge of leading his party but then his best friend lets him down. The lesson is: everyone is selfish. That friend you think is being nice? He's just doing it because he wants something. That relative who lends you money or gives you a present? He's doing it because he expects something back. There is no such thing as a selfless act.