We happy two: Jamie Parker and Tom Hiddleston tackle Shakespeare's Henry V

"The first time I did it, I lost my voice," recalls Jamie Parker. "Completely blew it on the first try, shouted my head off and lost it. Pathetic, really but you get carried away."

"It was the first scene we shot," Tom Hiddleston joins in. "I had to gallop along the moat of Arundel Castle with a cannon firing behind me, jump off my horse and address the army who were retreating having just had boiling oil poured on their faces. There were 30 tremendous, salty extras with me that day and I had never met any of them in my life before. I remember thinking, 'This is for me, this is for you, this is for all of us...'"

If this all sounds a bit dramatic, that's because it has to be. Hiddleston and Parker, two of Britain's brightest acting talents, are sitting in the wooden stalls of Shakespeare's Globe on a rare sunny morning, comparing notes on the stirring, throat-shredding "Once more unto the breach" speech that opens Act III of Henry V. Both can currently be seen playing Shakespeare's heroic monarch – Parker on stage at the Globe and Hiddleston on television in The Hollow Crown, the BBC's acclaimed series of History Plays produced by Sam Mendes. Parker's is a hearty monarch, leaping into the groundlings, joking about the rain, but always ready with a rallying roar or sober speech. Hiddleston's is rather more refined in a tight leather doublet, galloping on horseback and growing into his kingship frame by frame.

For both, it's the biggest leading role of their careers so far; the biggest, Parker points out, in Shakespeare, beating even Hamlet with over 1,800 lines, "if you string together Henry IV, parts 1 and 2 and Henry V". Both have done the triple whammy – Parker played Prince Hal at the Globe in 2010 while Hiddleston appeared in Richard Eyre's Henry IV earlier this month before taking the lead in Henry V, directed by Thea Sharrock. "It's one of the greatest journeys you can play – from wayward, wild, rebellious youth to compassionate, intelligent warrior poet," says Hiddleston. "I've always dreamed of it."

They are just two of a horde of Henrys currently cutting a swathe through theatres. Propeller has just brought its macho take back to Hampstead Theatre after a national tour, the Iraq war inspires a modern-day version at the Old Red Lion theatre in north London, while Theatre Delicatessen's Falklands-flavoured promenade production has just ended a run in a former BBC building on Marylebone High Street. And last month the Michael Grandage Company announced that Jude Law has signed up to play the monarch in the West End next year.

It's not hard to see why the play, centred on the English triumph over the French at Agincourt, with its patriotism, "band of brothers" underdog spirit and even a romance with a beautiful Princess Catherine, has captured the imagination in 2012. "You've had seven [History] plays of everything going to hell in a handcart and then Shakespeare finally dares to write a play about everything coming together. I'm not a royalist and I'm not a practising member of any kind of church but this play pushes my buttons," says Parker, stabbing at the air.

Laurence Olivier's flag-waving film of 1944 was commissioned during the war as a rallying cry but the play, which portrays the gore of war as lustily as the glory, has always been a more complex treatise on patriotism. Each generation has looked to it to comment on their own conflicts – from Agincourt to Afghanistan. Still, says Parker, it's not unusual for over-excited groundlings to join in on crying God for Harry, England, and Saint George. "Yesterday two guys in the gallery turned up with a St George's flag."

Hamlet aside, Henry is the dream role for a thirtysomething thespian – more muscular than Romeo, more heroic than Macbeth and, naturally, more vigorous than Lear. "It's about being on the threshold of manhood. It speaks deeply to parts of the male psyche," says Parker. And putting it on television, with Hiddleston, better known as Loki in Thor and The Avengers, is likely to bring it a new, generation of fans. "Thea talked about doing it for her 14-year-old nephew who loved Gladiator," says Hiddleston. "Most teenage boys are stewing in those ideas of masculinity. They want to be noble, to be men, but they're not yet."

From Shakespeare to superheroes is not such a leap, he says. "When I started playing Loki, Edmund in Lear and Iago in Othello were my touchstones. Two impeccable bad guys, let's throw in a bit of Cassius from Julius Caesar, a lean and hungry look and we're off to the races. I think Ken Branagh was consciously tracking the journey of Henry V when he was thinking about Thor."

Hiddleston and Parker can now add their names to an illustrious list – Richardson, Olivier, Burton, Dalton, Branagh – of Harrys on stage and screen. Do they feel the weight of history? "As an actor, it's completely terrifying," says Parker. "It's graduation day." "'Uneasy lies the head that wears a crown,'" says Hiddleston, quoting Henry IV. They both do this a lot – a by-product, no doubt, of learning all of those lines. "I was uneasy. I didn't get a lot of sleep. I knew that it rested on my shoulders."

Both actors arrived at the part with impeccable credentials. Parker, 32, was one of the original History Boys alongside James Corden and Dominic Cooper and went on to a role opposite Tom Cruise in Valkyrie before returning to lead roles at the Globe and the National.

Hiddleston, 31, also started out in the theatre, though recent roles have been in film, from War Horse to Midnight in Paris, in which he played F Scott Fitzgerald. He was playing Cassio opposite Ewan McGregor in Othello at the Donmar in 2008, when he was spotted by Kenneth Branagh, who has been his mentor ever since. Having co-starred in Cyrano on Radio 3, Hiddleston played Branagh's sidekick in Ivanov in the West End and the BBC's Wallander before Branagh cast him as Loki in Thor, a role he reprised in The Avengers. Now Hiddleston is playing the part that made Branagh's name on screen in 1989. Does he worry about comparisons? "I don't feel any pressure to be him. I worked with him a lot, he gave me a huge opportunity and then I go and play the part that made him famous. I'm very aware of it. I think he is too. He said he can't wait to see it."

Did he ask Sir Ken for advice? "No, I didn't think it would be helpful to either of us. All of us are standing on the shoulders of our predecessors. He knew he was a generation behind Olivier, Gielgud, Richardson, Schofield. We're the generation behind Branagh, Russell Beale…"

"And Rylance," adds Parker. By the time he finishes his run at the Globe, he will have performed the play some 110 times. "It can be a cruel and frustrating mistress," he says. "If I come on and I'm just imitating my vocals and movements, it's completely exhausting and the audience is bored. But if you catch the wind…"

Hiddleston's endurance test was a four-month shoot of all three plays back to back last winter. "Out there in chainmail, on horseback, shooting battles. My hands were absolutely ruined, my knuckles were split and bleeding from being outside and fighting every day. You think, 'I am reliving this'. Your imagination has to supply less of the detail, but at the same time I didn't have the live audience backing me up."

"I'm really envious of Jamie doing the whole thing every night", he adds. "And I'm really glad that I don't have to be filming it every night. The stamina required… I was on the floor after the shoot."

Post filming he collapsed and headed to Maui "to sit on a beach and watch whales". Parker, who has a one-year-old son with his wife, the actress Deborah Crowe, is also planning a break, come September. He's currently writing a book about his experiences playing Shakespeare. "It feels like the end of an era. It's been such a long time coming so finally having scotched it, it feels like whatever comes next should be different. Which is not to say that I want to stop acting – it's my lifeblood – but it's time to pause and reflect."

He will next be seen in the British screwball romcom Le Weekend and the BBC/HBO period drama Parade's End, playing a socialite "who is constantly nipping at Rebecca Hall's heels". For Hiddleston, it's straight to Detroit to film Only Lovers Left Alive, a vampire romance with a twist. "Playing a vampire for Jim Jarmusch is an entirely different thing..." Then it's back to Loki in Thor 2.

They will both miss being a king. "It's a part with which you can light fires under people," says Parker. "The experience of playing it is one that changes you permanently," agrees Hiddleston. "The intelligence, compassion and wisdom in the writing pulls you in. You carry it with you until you die."

'Henry V', Shakespeare's Globe, London (020 7401 9919; shakespearesglobe.com) to 26 August; 'The Hollow Crown: Henry V', Saturday , 8pm, BBC2