I really wanted Tom Hanks to look Muse (Abdi) in the eye and say 'Walt, you've gotta call me Walt', but that's just the risk these megastars run when they appear in two completely different movies at the same time.

Other than that, everything you've heard about Captain Phillips is true. The sense of urgency and menace is like a throbbing heartbeat throughout the whole film. It's incredible how much tension and conflict Greengrass' style and Billy Ray's script can wrangle where there's no real antagonist – certainly no evil bad guy.

As the movie is at pains to make clear, this is just a story of colliding interests. Whether they go offshore to fish or point AK-47's at container ships to ransom off the crews, Muse and his contemporaries aren't that much different from Phillips – you get up in the morning and do what you can.

We meet them both on opposite sides of the world as they prepare for a workday – the former being recruited on the beach by gun-wielding thugs working for a local warlord, the latter driving to the dock talking with his wife (Keener) about their kids.

But when the tiny dots appear on the horizon, Hanks the Oscar winner comes to the forefront. The worry lines never leave his face as the hoses are turned on and the gang of four boards the Maersk Alabama, quickly overtaking the gigantic vessel. Phillips is smart enough to send most of the crew to hide while he and the few men left scramble to think of something, all while watching the impoverished and desperate-looking men draw closer.

I was surprised by how much of the film took place in the little yellow lifeboat rather than on the container ship, but it's there in the cramped, sweaty confines that the tension goes through the roof. Two US Navy warships are called in and the sights of drones, choppers and rifles are trained on the tiny bobbing craft, Phillips counting the seconds of his life away inside as his captors grow increasingly aware how out of their depth they are.

The climatic device – of the SEAL team trying to line up the sharpshooters to bring the situation to an end – is the kind of thing to prompt grudging respect for the professionalism of the American military (when they wield it for an honourable end), and it's surprising looking back Hanks wasn't nominated for an Oscar. His shell-shocked Phillips during the final scenes is as effective as McConaughey's weight loss for Dallas Buyer's Club. It's an action movie that's so realistic and affecting it spills effortlessly over into drama.