Actor Mark Rylance’s work ranges across film, theatre and television, including the BBC’s recent Wolf Hall. He also served as artistic director of Shakespeare’s Globe from 1995 to 2005, and his own play, Nice Fish, will be performed in London’s West End this November. He plays the title role in Steven Spielberg’s film version of The BFG, and earlier this year won an Academy Award for his supporting role in Bridge of Spies. Rylance is due to appear in two more Spielberg films, Ready Player One and The Kidnapping of Edgardo Mortara.

Steven Spielberg approached you about playing the Big Friendly Giant when you were filming Bridge of Spies. Was it a shock?

Of course. Wouldn’t you be surprised? It was only the first or second day. I was still dealing with being around Tom Hanks and Steven!

And it’s rather different from the work you’ve done previously…

The motion-capture is. The BFG’s interesting because I did a play in London called Jerusalem, which had me in the middle of it saying how I’d met a giant and we’d gone to Stonehenge and talked for a while. And then, at the end, me banging a drum and calling in the giants. So I was amused when Steven offered me the part, and I thought, “Well, that’s a very amusing twist of fate that I will now be a giant myself.”

You star opposite an absolute newcomer, 11-year-old Ruby Barnhill. What was that like?

Pretty much all children are helpful to act with; they lack any guile when they act. Ruby was particularly helpful: very, very present. And you also hear the very useful basic instructions that Steven would never say to Tom Hanks or to me, but he says to her: “Now concentrate, take your time before we start, just get into character, feel and think what’s going on.” I’m doing that anyway, but it’s great to be reminded. Steven’s got such incredible performances out of children; understands them so well and loves them so deeply, loves their imagination and energy tirelessly. So I was really very happy to be quiet and watch that. And then our [Mark and Ruby] relationship really came together when we were on screen.

One of the most striking things about the BFG is his words: delumptious, frobscottle, whoopsey-splunkers. You so often seem to work with interesting language. Is it conscious?

Just through chance I’ve had a lot of experience with difficult language, and so if there’s a part that has a challenging language thing, then that’s probably the right place to put me. I like words.

And that, of course, extends to Shakespeare.

I didn’t particularly aim to be a Shakespeare actor, but I suppose I had a certain gift for it; I certainly got offered lots of it. I liked Complicite and Shared Experience and Kick Theatre, and all the small theatre companies that were getting going. I wanted to be like that, making original theatre. And I liked Buster Keaton and silent, physical stuff. I’d grown up with the RSC, but in the early 80s it wasn’t really my ambition to be so much part of that. And then I got pulled into it, and it was a fantastic company of actors and plays. And then one thing led to another and I ended up at the Globe.

You were there for a decade. What was its impact on you?

It was a very intense period but very exciting, with some of the happiest times I’ve ever had in the theatre. On a good evening or afternoon there, you know, there was nothing like the connection of the audience and the actors. I remember at the end of Antony and Cleopatra. It’s raining, a cold Sunday afternoon, and I look down and I see four or five old women, 60s, 70s, 80s – I shouldn’t say that’s old now, I’m nearly 60 – but they’re not like 20-year-olds, and I see, my God, they completely believe that I’m Cleopatra. And yet I’ve got nothing – there’s no lights, I’m standing on a rough platform, about to kill myself, and they’re all still. It was amazing. It was like surfing, or gliding. What’s holding us all? Just imagination. The story has taken us all to this place. All the scaffolding’s gone, all the training wheels, everything that was to get us there has gone. It’s just us, floating in these last moments of the play. It was a very extraordinary experience to be inside that.

You are celebrated for capturing that stillness at the heart of characters – most recently, Rudolf Abel in Bridge of Spies and, of course, Thomas Cromwell in the TV adaptation of Hilary Mantel’s Wolf Hall. Will we see Cromwell again?

It’s very exciting her writing the next book. It’s going to go back over things, I think, and show a different perspective. So I imagine that you’ll get to the execution of Cromwell, and you yourself as a reader or a viewer may not be so certain any more. As soon as she’s got the book finished to her desires, the brilliant woman, then Peter Straughan will be set to make a new script.

Your body of work includes such interesting reflections on nationhood, and Englishness: Johnny ‘Rooster’ Byron in Jerusalem, Cromwell, the adaptation of Paul Kingsnorth’s novel The Wake – the story of the aftermath of the Norman invasion, told in Anglo-Saxon-inflected language – you’re working on with your wife, Claire van Kampen. How has that affected your outlook?

We were working on The Wake, Claire and I, during the whole Brexit vote, and it really reminded me of the narrator’s outrage when William the Conqueror happens to win the battle at Hastings by a fluke, by an arrow hitting the king. How deep this distrust and anger towards Europe and France goes back. Because, my God, when you read The Wake, or you read any history of William the Conqueror, you never love those castles any more. Ever since, whenever I drive by a castle, I realise that there was a time when England was a prison camp, a very violent prison camp, with a language forced on it and everything suppressed.

Can you relate that to Britain today?

It was so fascinating to go back and see the deep, deep wound of that invasion. I think to some degree it still resonates in the English psyche; a distrust of relationships with Europe, that somehow we will not be treated fairly, that we will have things imposed on us. My understanding is that we are generally a very philanthropic and compassionate people – that when there are disasters in the world, individual citizens send loads of money into appeals for different things. We’re a bloody violent people, football fans, and we’ve been successful at wars, and we sell far too many weapons. But we’re also very philanthropic, we’re imaginative in science and the arts, and about other people. So this toxic subject of refugees and immigrants is not necessarily true to the deeper character, I don’t think.