The only thing missing is By the Sleepy Lagoon. Aware that this is probably the closest I'll ever come to being a castaway myself, I quietly lap up the atmosphere as I sit in the Desert Island Discs studio at the heart of Broadcasting House in London. A few feet away, Kirsty Young and her producer pore over a computer screen.
"Well, it's goodbye to whatever you used to do on Sunday morning after listening to the show," says Young as she crosses the room to give me her full attention. "For anybody who likes the game of the show, this is hours of endless fun. I'll be on the computer doing it with everyone else."
The "game" is cross-referencing the song choices, books and luxury items of the 2,800 or so castaways who have appeared on the programme since 1942 with your own selections. It's played on the new Desert Island Discs online archive, a searchable database that holds 69 years of fascinating information, provided by the guests of one of the world's longest-running radio programmes.
You can explore it yourself at bbc.co.uk/radio4/features/desert-island-discs
"Bruce Oldfield and I have a connection. We keep choosing the same things," says Young excitedly, as we talk about her favourite songs.
The archive allows users to search by musical choices, book, author, castaway name or luxury item. Want to know which guests selected songs by the Byrds? Click. AA Gill, Chris de Burgh and James Fox. Interested in Nick Clegg's luxury? Easy. It was a stash of cigarettes.
What's more, much of the modern archive - around 500 shows from the past ten years - can be listened to or downloaded from the website.
"The fact that you can cross-reference is the addictive thing," says Young. "Chris Evans has got one of my tracks. Once you've got your eight choices, the first thing you do is start searching."
It's taken over a year to collate, sort and "clean" the seven decades of data on the site. In excess of 22,000 pieces of information have been garnered from dusty books, files and rudimentary databases before being crosschecked (cleaned) with the books of Roy Plumley (show creator and long-time presenter) and back issues of Radio Times.
There are surely few other radio programmes that the BBC would go to such an effort to archive, so what is it that makes Desert Island Discs such a popular and enduring show?
"It's the format. I think the format's elastic," says Young, who took over presenting from Sue Lawley in 2006. "Interviewing people, it's very difficult to get to a place of intimacy, and music immediately gives you that intimate bridge.
"Sometimes there's almost physically a sensation when people are listening to music in the studio, their shoulders go down, they cock their head, and you can tell for a moment that they're somewhere else. And that's a gift as an interviewer."
She explains how the programme's "ingenious" set-up allows it to shrink or expand effortlessly to accommodate anything from a relatively straightforward interview to "a David Walliams moment". Indeed, in nearly five years Young has drawn a number of high-profile on-air confessions from her castaways, including Walliams, Yoko Ono and Kathy Burke.
And she believes that there are few places left in the modern media where enough space is given to truly contextual interviews.
"I'm a real enthusiast for the long-form interview," she explains. "I think it's a shame that we've lost something in the culture of immediacy that allows you to actually be in conversation. The best sort of Desert Island Discs programme is when you feel like the third person in the room - a triangular conversation with the listener."
Did she feel under pressure being appointed custodian of such an important part of British radio history, only the fourth after Roy Plumley, Michael Parkinson and Sue Lawley? "When I started, yes. I said at the time, it's like somebody handing you the family china that your great-great-grandmother left and then saying, 'If you could just run for a mile with that and not trip.'
"You immediately feel the sweat dripping down the back of your neck. I don't feel that at all now, but at the beginning I felt the weight of it."
Young admits that some castaways are more nerve-racking than others. She describes the challenge of interviewing great academic luminaries such as mathematician Marcus du Sautoy and concedes that although they don't intimidate her, "politicians are also difficult" because "you're always trying to wrestle them to the ground to try and make them loosen up a bit."
But getting through the tricky moments comes with its rewards. "I think I said it during Tom Jones's programme - I love this job. There are moments where it's as close to being in intimate conversation as having dinner with them. It feels like just the two of you. The best type of programme is when I have a plan in my head, and I end up abandoning it."
And plan she does. Young regularly spends days reading up on her castaways. "Research is a really big part of it. It's a gift, an absolute education…" she says.
"If someone's an author, you want to have read at least their big two or three books, so that's a week or two's homework. With Martin Sheen, I watched The West Wing." What, all seven seasons? "I didn't watch the whole of The West Wing, but I watched a lot of The West Wing."
If she could have interviewed any castaway, ever, who would it be? "Oh, Louis Armstrong would have been wonderful. I remember Sue doing a brilliant job with Armando Iannucci, who I'm a big fan of. And being Scottish as well, that would've been very interesting. He's one of the best writers around. I'd have enjoyed that."
Young ponders for a moment. "But way back, hmm, there must be people…" She crosses to the computer and begins scrolling through the archive. "This'll just make me depressed, seeing all the people I've missed now…"