Halfway through the BBC‘s exceptionally fine new drama series Bodyguard and, like the principal charters, the show is retaining is composure despite the intense strain of events.

Curiously, in episode three we found ourselves warming to the cold home secretary Julia Montague, played with great plausibility by Keeley Hawes.

She started out pretty unlikeable on any level, but now, with a couple of assassination attempts behind her, we’re starting to care a bit more about whether she lives, dies or becomes prime minister after all.

Some of that, of course, is down to her affair, if that’s the right word for it, with her personal protection officer, Sergeant David Budd (Richard Madden). Whatever is going through his mind as he protects her, from loneliness as much as assassination, she, it is now clear, genuinely cares for the hunky copper, rather than just using him as “room service”, as he called it.

I didn’t really get the impression some seem to have formed that he is some sort of emasculated male being kicked around by a lot of women bosses, which Montague does suggest. I think it’s just that he is a bit down about being used sexually.

Contrariwise, we still don’t know if, or how, he might be using her. At some points he does engage in limited surveillance of her activities – as demanded by his police chief (Gina McKee) as part of her vendetta against Montague. Then again, the rest of the time he chooses to say nothing, or lies for her.

It doesn’t look as though Budd is some sort of covert assassin himself, but there’s still a sliver of doubt about whether he is playing some sort of long game. He is after all, literally and metaphorically scarred by his wartime experience in Helmand, a conflict Montague voted for, and his PTSD is brought dramatically to the surface when she wakes him from deep sleep and he almost strangles her. That was a scene that shouldn’t have worked, because, honestly, it is a bit far-fetched, but Hawes and Madden made it feel natural, if weird. Just right.

So we’re beginning to feel some emotional involvement with Montague, especially. She’s developed a little humour, as when she remarks “sex with the Home Secretary; it’s a heinous crime”. (My racing mind summoned up a graphic and disturbing image of Sajid Javid).

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Montague’s politics too, seem more reasonable, or at least comprehensible, once she is heard making the case for shredding civil liberties and, unimaginable for a 2018 Tory, advocating for more social mobility in important prestigious profession such as the law, politics, medicine and, er , journalism (thanks for that). There also seems – seems – to be something awry with the prime minister, in which case her ruthless ambition is developing a more ethical quality. Could he be the cocaine and alcohol addicted sex maniac she is being secretly briefed about by the security service?

One of the many great features of Jed Mercurio’s deft screenplay is that the unremitting focus on the two leads makes the many complexities in the story easy to follow, especially for the jaded viewer looking for a little diversion before the working week winds up again. At every turn you, like the eponymous bodyguard, feel motivated to scan the screen for potential plots and threats.

The source of the latest near-fatal attempt on Montague, probably a suicide bomb, wasn’t clear at the end of episode three – classic cliff hanger – with a choice between a rogue police officer, a BAME special adviser or other person or persons unknown.

The suspense with Budd derived from his double dealing between his police bosses and the scrutiny services, and his protection of a former army comrade who tried to shoot Montague dead. There was a claustrophobic sense that Budd’s lies about his old mate are about to be found out, as the clues to his identity and background build up.