In the National Theatre’s current production of Hamlet, heavies guard the doors of Elsinore Castle. Squiggly wires rise from their collars, feeding security information into their earpieces. Overhead, CCTV cameras watch every move.

This is indeed a modern, grey and scary world, heightened by the fact that Patrick Malahide, playing Claudius, looks arrestingly like Vladimir Putin.

“It hadn’t crossed my mind at all that he looked like Putin!” laughed Rory Kinnear, who plays the title role.

“Then everybody started saying it. I realised what a stroke of genius I’d stumbled on!”

We met backstage after a matinee performance, and Kinnear seemed remarkably relaxed, in spite of having just stepped off the stage after a gruelling three-and-a-half hours playing one of theatre’s most demanding roles.

What, I asked him, was his reaction when he was first offered Hamlet?

“It was about three years ago, and I was doing a show called The Man of Mode with Nick Hytner [director of the National, and of this production].

“He called me into his office, which I presumed meant I was going to get my papers, and something like, ‘thank you very much, but we don’t need you again’.

“But, instead, he had two future projects in mind, one was The Revenger’s Tragedy the next year, then he said, ‘in the shorter term, there’s the question of Hamlet. I’d like to do it with you’.

“I was 28 at the time, and I’d never really thought about it. I had never coveted the role — I don’t particularly covet roles anyway, because it’s upsetting if they don’t happen. Then if you do want something, and try to shoehorn yourself in, you might not be right for it.

“I think it’s the director’s decision whether or not you’re right for a part. So it wasn’t something I’d lusted after, but obviously when he asked me I started thinking about it.”

Unusually for a production that began in London, the National Theatre has now sent Hamlet out on tour across the country with absolutely no changes to the original cast.

When we spoke, Kinnear had been playing Hamlet for several months already, to very considerable acclaim. Obviously, he’d worked his way more into the character as the London run progressed.

But was he still discovering new things?

“Definitely. It’s a part that many actors return to again and again because they consider it unfinished business. There’s an endless and kaleidoscopic richness to the part.

“The frustrating thing about doing a production of it is that you have to make decisions. Studying it, you can say, ‘Shakespeare could mean this, but if you did it in that way, it could also mean that’.

“It’s the kind of elastic play where if you got the same group of actors and director in a room now rather than seven months ago, the atmosphere in the room would be different enough to create a different production.

“Come the last performance, I always want to apologise to the audiences who came to see it at the beginning, because you’ve made so many more discoveries, and you’ve got a richer and deeper understanding of your character.

“If you see the whole life of a play, from the first day of rehearsals to the last performance, the first time in front of an audience is a bit like going to university: you’re leaving home, but you’ve still got a rich life ahead of you, hopefully.”

Kinnear’s Hamlet is an infinitely complex man. But he also displays an evident sense of humour.

So are Hamlet’s signs of madness wholly an act?

“Having seen the ghost of his father, were he to return to court as the same rational, logical man that he was before — the doors of his experience of life having blown off — he wouldn’t be able to do it.

“So why not go to the opposite extreme, and pretend to be a lunatic, so people will dismiss him as just having gone loopy? He’s probably taking it to the wire, seeing how far he can go with people. On the other hand there’s the attendant depression and sense of self-loathing.”

lHamlet is at Milton Keynes Theatre from March 1 to 5. Tickets: ambassadortickets.com/miltonkeynes or 0844 8717652.