At 70 years old and with a filmography as lustrous as his peculiarly bouffant hair, Christopher Walken has evolved a simple checklist for picking scripts.

“You want to get a script where you’re given good words to say and it’s intelligent and it comes out. One where you’re saying interesting things. But I don’t get a lot of those.”

That, says the venerable Hollywood grandee and indelible totem of movies from The Deerhunter to Pulp Fiction, is why he signed up for Turks & Caicos, the second part of playwright David Hare’s modern spy trilogy for BBC Two.

The first film, Page Eight, was Hare’s attempt to lay bare the troubling consequences of the War on Terror. It followed disenchanted MI5 agent Johnny Worricker (Bill Nighy), whose discovery of a document revealing Downing Street’s knowledge of torture as a means of obtaining intelligence forced him to flee the country. In Turks & Caicos, we catch up with Worricker in hiding on the tax haven islands of the title, where Walken’s character, who may or may not be an undercover CIA man, drags him into the company of a group of sinister American businessmen with links to the security services.

Hare gets his point across about international corporate and government skulduggery while we get to enjoy a series of delectable scenes in which Walken and Nighy circle each other, crumpled and vital and incorrigible all at the same time.

In real life, meanwhile, Walken and Nighy seem to have formed a mutual appreciation society (“Christopher Walken? I’m obsessed,” said Nighy at a recent press launch). “I just love him,” says Walken. “I wish everything I did he was in. That thing they talk about with actors, that elusive chemistry whatever that is? It’s a real thing and you can see it.”

It helps that Walken and Nighy have matching strengths ? pregnant pauses, languid delivery, ineffable style. Walken says his approach to acting is long established: he likes to sit back, read the script, swill it around a little.

“I put the script on my table and I read it over and over and over… It grows from there until it starts to make its own kind of sense to me. Sometimes it doesn’t happen which is tricky, but most of the time something starts to crystallise. [In this instance] then later on David [Hare] and I spent time sitting and talking and working things out.”

I am intrigued by the image of Walken, Nighy and Hare sitting around a Caribbean hotel bar, perhaps with a Scotch and a cigar, pinging anecdotes, chewing the fat. Did they talk politics? Hare’s position on the left is fairly unequivocal…

“He and I didn’t talk about that.”

So how did the conversation run?

“In my life, when I was young, all through my career, in working with actors in particular, because they’re the ones who sit around waiting - it’s interesting that no matter what the movie is about or to what extent one is involved in it, that mostly what actors talk about with each other are movies, restaurants, and when you’re younger, they talk about girls.”

^{Tailor-made: Christopher Walken in the Premium by Jack Jones campaign}

Nighy and Walken can still cut a dash. In Walken’s case the eyes that bore right through now come with a tinge of dolour, but that only enhances their depth on screen. I bet, I say to him, that they still talked about girls ? in spite of the fact that Walken has been married for 45 years to casting director Georgianne Walken (Nighy lives alone).

“Yeah, yeah, sure we did. Plus Bill is hilariously funny and he’s very aware of comics, too, so we talked about that. I would tell him a lot of [US comedian] Rodney Dangerfield stuff which would practically put him on the floor.”

With that breathy, wizened voice for which he’s so often mocked, you might not have Walken down as the comedian. But in the US he’s as well known for his self-mockery as his stagecraft. We don’t show Saturday Night Live over here, but it is a comedy institution in America and Walken has hosted it seven times, more than anyone other than Alec Baldwin, Steve Martin and Tom Hanks. He also generated millions of views on YouTube as the twinkle-toed dancer of Spike Jonze’s video for Fatboy Slim’s ‘Weapon of Choice’.

“My early life was in musical comedy theatre and I’ve always kept that. I think it’s kind of my basic training and I’ve always been very aware of comics and what they do. There are a few things on my bucket list that I doubt if I’ll ever get to do. One is driving across America. But I’m a terrible driver, so that’s probably not a good idea. The other is doing a stand up comedy routine, just me in front of an audience with jokes. But I’ll probably never get to that either.”

Not only have British audiences not seen Walken be funny that often; but we’ve developed a very different sense of him from his most enduring roles.

“If you’re lucky something early on in your career works and a lot of people see it. You kind of get known for that and it gets you going,” says Walken. “In my case, it was The Deer Hunter and Annie Hall, which came out within six months of each other. In both of those films I was a suicide really, a guy who is quite disturbed. A lot of people saw those performances and I think I started getting those kinds of parts, but it has nothing to do with where I started from. I started being good at being silly in musicals. I think I have a powerful silly streak. It’s just part of me. It’s how I made my living until I was about 30.”

The intriguing thing is that for Walken, the silly and the serious are all part of the same whole. He thinks that the lingering menace that characterises some of his best work is closely allied to his sense of humour.

“The menace thing has to do with villains and playing them so often in movies, but I have a notion that there is some intrinsic ancient connection between what’s funny and what's scary - that our ability to get scared is somehow related to our ability to find something funny. There are things that can’t really be explained, like the human laugh - what is it about? Where does this come from? It’s been suggested that the human smile is really a baring of teeth - that it’s a warning. I think these things may be somehow linked.”

They may be most closely linked in Christopher Walken’s smile, one of the most unsettling sights on screen. It’s a smile that also endows him with an inscrutability that is a perfect fit for the murky, unnerving man he plays in Hare’s drama.

Turks & Caicos is on BBC Two on Thursday at 9pm