The day I visit, it is clear just how far the poor troglodytes inside are starved of contact with the outside: sighting a face that still bears traces of wind and sun, Howard Brenton cries out: "What news?" - this is the day that Bill Clinton's videoed testimony before the Grand Jury is due to be released.
There is a small irony here. While the fate of one world leader hangs in the balance outside, in here we are observing the downfall of another: Anthony Eden, one of the central characters of Brenton's play Nasser's Eden. The play takes place over 10 days at the height of the Suez Crisis of October 1956. The subject of Suez has, Brenton says, gripped him for years:
"I've a memory of being in a playground when I was 14, and fights breaking out for and against Egypt. There weren't many of us supporting Egypt."
He considered the notion of a stage play for some years, and did all the research and thinking. But he could not come up with a way of dramatising what he saw as the affair's central relationship, between Sir Anthony Eden, the patrician British prime minister, and Gamal Abdel Nasser, the upstart nationalist leader of newly independent Egypt - especially difficult given that the two men met only once, and that was some time before the crisis.
But when he was approached by the BBC with an offer to write a play on any subject he liked, the unwritten Suez play sprang to mind immediately. "I thought, you could get inside their heads, use their voices and cut very quickly one to the other, and that could work very well on radio."
So Nasser's Eden is an unusually concentrated, fast-moving radio play, jumping between London and Cairo with an almost stroboscopic speed, never letting its two central figures out of earshot.
Remarkably, after a career spanning 30 years and at least as many plays - including such landmarks of modern theatre as The Romans in Britain and Pravda - this is the first play Howard Brenton has written specifically for radio (though several of his stage-works have been adapted). It is also the first time he has gone into the studio with a play; but he seems to enjoy the experience. One reason for that is the sort of cast you can get for radio. On the first day's recording, devoted to the Egyptian scenes, the cast included Nadim Sawalha as Nasser and Saeed Jaffrey as Nehru. On day two - the London scenes - when I go along, it includes Alec McCowen as Eden, plus Bob Peck, Nigel Davenport, James Laurenson and Trevor Peacock. Most theatres would kill to get that sort of company; and then they wouldn't be able to pay their salaries.
Quite why actors want to do radio seems a mystery, watching Alec McCowen at work. The way the play is structured means that he is under extreme pressure, stuck all day in the ramshackle, dot-to-dot realism of a recording studio - real telephones for ringing and picking up, real glasses to clink and real doors to open and shut, but marooned in a warehouse-like space strewn with corporate plastic chairs and odd bits of carpentry. And the actor is always being watched by the shadows behind the glass, with every now and then a voice (like the sprouting phones in Teletubbyland) issuing orders - "You're playing it too low-status." In the event the recording session overruns until after 10 o'clock.
But this is one reason actors like radio: as Cat Horn, the play's producer, points out, you only have to get things right once, and even then it needn't be a whole scene. And there are some other attractions: "You don't have to worry about bumping into the furniture and messing up the props." Brenton adds a couple of other suggestions: "They don't have to spend weeks learning, and they don't have to spend hours worrying about what they look like ... and it's all done very quickly and everyone is hearing what everyone else is doing, and an ensemble spirit is formed very quickly and then dispersed. It is a two-day bubble."
Certainly there is plenty of camaraderie in the studio. When I arrive, in mid-afternoon, the green-room is buzzing with anecdotes ("...and it must've cost them 15 grand to fly him out, put him up for two weeks, fly him back!"). Horn says it helped that they started the day by getting all the actors to be an Egyptian crowd, and they had a good time hawking and cheering and shouting: "Allah akbar" (though on the finished tape it all sounds more restrained than that).
Even leaving aside the actors and the company spirit, working in radio has a more fundamental appeal to Brenton: "The craft is always a delight, and it was good to take on a new form."
Horn reckons that, this being his first go, Brenton hasn't tried to stretch radio to its limits; certainly he doesn't use the cinematic flexibility of focus or the wild visual flights that invisibility permits. That's partly down to his personal conviction that radio does have visual limitations: "I think you've got to see it in your head very clearly. If it's well written, you immediately see the room people are in."
But if he doesn't stretch the form in some directions, the narrowness of focus in Nasser's Eden is appealingly different: "I love telephone calls on radio, and I love voices being very close to you... I was interested in when they breathe or not." (McCowen, with his almost Ned Sherrin-like mastery of the pause, was clearly natural casting.)
And even the limitations of radio have their appeal for the first-time author. Brenton instances the fact that, "I had to put names in more than you would on stage so that the listener always knows who is speaking. And that is a particular piece of radio crafting you've got to learn."
I wonder if he found it difficult to do this, but he insists not. Listeners, on the other hand, hearing one dignitary addressed as "You, an admiral, the great Mountbatten", may feel that he has still has a little way to go before he has mastered the trick of integrating information into natural- sounding dialogue.
In the meantime, after the grand spectacle of plays such as The Romans in Britain and Moscow Gold, his controversial account of Gorbachev's dismantling of Communism, Brenton is enthused by the idea of "momentous events presented in intimate details", and even contemplates making Nasser's Eden part of a trilogy on turning-points in post-war Britain:
"You would have Aneurin Bevan creates the Health Service, the second is Suez, and the third would be impossible to write, because it would be Thatcher coming to power. That would be impossible because they're still alive." Still, it's nice to dream.
'Nasser's Eden' is on R4, Fri, 9pm