Collateral series finale gives us a bittersweet, compelling conclusion

• Meet the cast of BBC2 thriller Collateral
• Jeany Spark on the "traumatic" past of key Collateral character Sandrine Shaw

But in the final episode, all these threads start to pull together and the convoluted story becomes clearer. That's not to say that the threads wrap up neatly into a little bow – but there is a satisfying ending, of sorts.

Here's what happens:

Carey Mulligan's DI Kip Glaspie saves the day

It is Carey Mulligan who carries this series and makes Collateral such an enthralling watch. The Oscar-nominated actress is excellent as a determined detective with a wry smile and a plan, who keeps her cool and her counsel.

In the final episode, she's in trouble with her boss: to get the information she needs about the people-smuggling operation and why Abdullah Asif (Sam Otto) was assassinated, she might have made a promise she can't keep. Specifically, she offered UK residency to Fatima and Mona Asif, the two Iraqi illegal immigrants. Oops.

But don't underestimate Kip! She obtains footage from Fatima's phone and identifies three people smugglers – Mehmet (George Georgiou), Bhuran (Guy List), and finally a woman named Berna Yalaz (Maya Sansa). Mehmet and Bhuran are arrested, but Kip has a hunch about Berna: is she an undercover MI5 agent? That would explain the way security service bloke Sam Spence (John Heffernan) is behaving.

At the police station, Kip conducts an off-the-record chat with Berna and obtains the identity of the British people smuggler. Case closed! And even better, Berna is her bargaining chip with MI5: in exchange for her release, the Iraqis get to stay.

Sorted! (With, um, a few caveats. See below.)

Snobbish MI5 man Sam Spence is outwitted

John Heffernan is so, so good at playing twits and bastards and pompous know-it-alls. In The Crown he is the Queen's critic Lord Altrincham; in Outlander he is sneering Redcoat Lord Thomas; in The Loch he is unpleasant doctor Simon Marr. In his hands, MI5's Sam Spence becomes the ultimate villain.

Sam forges a relationship with Kip's dissatisfied second-in-command, Nathan, who leaks information to him about Fatima and Mona and the investigation. But he dramatically underestimates Kip herself. She works out that he is leaking information to a journalist – but why? Because he's got a "cock in the fight"! In identifying and questioning Berna she outmanoeuvres him in such a satisfying way.

John Simm's self-pitying MP found a backbone

Even if you agree with his politics, shadow transport secretary David Mars (John Simm) has been consistently annoying since episode one. He is prone to lecturing his estranged wife Karen (Billie Piper) and yet never quite untangles himself from their disastrous relationship, letting her order him around and wind him up. He's also spent the whole series running away from Labour party leader Deborah Clifford (Saskia Reeves) and dodging her calls, instead delivering self-righteous speeches.

But in the final episode we finally, finally meet Deborah – and she is having NONE of David's lecturing. "On no account piss me about," she warns. When he protests that he's been preoccupied with a murder in his constituency, she shoots back with an eye roll: "Ooh and you can't multitask? Don't be a prick, David." He's sent away simmering with anger but with his tail between his legs.

And then, what a change! David makes a decision to finally grow a backbone and take charge of his life. He sacrifices his political career and skips a key vote; he ignores Karen's drama and leaves the flat after putting their daughter to bed. And he walks out the door to reconcile with his ex-girlfriend with a smile on his face. There's life in Mars after all!

Nicola Walker's lesbian vicar chooses the Church

Ever since the Bishop turned up in her kitchen with an ultimatum, Jane Oliver (Nicola Walker) has been struggling to decide what to do. Should she stay with her Korean girlfriend Linh (Kae Alexander), who is illegally in the country and was caught high on drugs when she witnessed the murder? If so, she'll have to give up her position in the Church as the affair risks becoming too public.

Ultimately, Jane chooses her vocation. Linh, angry and heartbroken, leaves. The murder ultimately led to this couple's break up, which is sad – but in some ways it's perhaps for the best. These star cross'd lovers never seemed to get along that well anyway.

Soldier and shooter Sandrine goes AWOL

Ever since she carried out the assassination on behalf of family friend (and secret people smuggler) Peter, Captain Sandrine Shaw has been unravelling.

She is struggling with the vivid memory of her friend's death in combat, and with her uncertainty over whether she has killed the right pizza delivery boy, and in episode two she is blackmailed and raped by her superior officer, Major Tim Dyson (Robert Portal). Sandrine grieves for her father and brother, but cannot talk properly with her mother. In short: she may be the murderer, but screenwriter Sir David Hare has done an excellent job of making Sandrine a fragile, damaged human with a twisted sense of honour.

In the series finale things come to a dramatic head. Sandrine storms into Major Dyson's house to warn his wife that he's a rapist and serial sexual harasser, before stealing her car at gunpoint. The reason for her reckless behaviour becomes clear: she doesn't plan to be around for long. Sandrine drives to a hotel, shuts herself up in a bedroom and writes a suicide note.

But Sandrine's chat with Mrs Dyson has a lasting impact that will destroy the predator's idyllic life. When the Major arrives home to comfort his wife after her ordeal, she looks at him with cold eyes and says: "The thing is, I believe every word she said."

Kip Glaspie botches her suicide intervention

By this point, Kip Glaspie has pieced everything together after interrogating Berna Yalaz (Maya Sansa): the soldier who the police have been told is AWOL from the Royal Surrey Artillery is, in fact, the same one who committed the murder on the orders of a British people smuggler. And that soldier is Captain Sandrine Shaw.

And where is Captain Shaw? Locked in a hotel room with a gun.

Kip arrives on the scene, goes straight upstairs and talks to Sandrine through the door. She seems to be making headway and connecting with Sandrine as she encourages her to talk about her childhood – but then she makes a terrible error: she lets the distressed soldier know that the man she killed wasn't a terrorist, like Peter had said. He may in fact have been a good man.

Sandrine pulls the trigger.

This was an unusual thriller in that we have known the murderer's identity since the end of the first episode. It wasn't so much a whodunnit as a whydunnit. Sandrine may not be a wholly sympathetic character, but hers is a sad story and subverts many of the usual "baddie" tropes.

Mona Asif has her baby – with Fatima at her side

We may have had two deaths, but the series ends with a birth. Mona Asif, who was raped in Iraq and forced to flee as a refugee, goes into labour at Harsfleet detention centre and is taken to hospital where she gives birth to a baby girl.

"Pimlico Travel" operator and people smuggler Peter Westbourne gets away

In the final episode the police work out that former military man Peter Westbourne (Richard McCabe) is a people smuggler, operating under the cover of "Pimlico Travel". But by the time the police raid his offices, he is gone.

With his Turkish henchmen in custody and his identity exposed, the game is up for Peter. But for now at least, he has escaped the consequences of his actions – so it's a bittersweet conclusion.