On a recent blustery weekend, the gallerist Robert Diament and the actor Russell Tovey, co-hosts of the British podcast Talk Art, had a deliberately untouristy agenda as they darted between three New York boroughs: recording upcoming episodes of their show, which has become one of the fastest-growing art-focused podcasts on the internet.

Since its first episode in October 2018, Talk Art has steadily built up a substantial following, with more than half a million downloads. But in spite of that popularity — and prestigious guests like the curator Hans Ulrich Obrist and artists such as Grayson Perry, Vik Muniz, and Toyin Ojih Odutola — the program has lost none of its initial unaffected, homespun feel. Mr. Diament, 39, and Mr. Tovey, 38, interview their guests with a wide-eyed gusto, whether they are captivated by gallery owner Sadie Coles talking about working with John Currin, or are listening intently to how Tracey Emin’s grief over her mother’s death inspired her recent show at White Cube in London.

The pair will be recording more episodes here over the next few months. Mr. Tovey is currently in New York to perform in a Broadway production of “Who’s Afraid of Virginia Woolf” that opens in April. Mr. Diament is planning several visits for podcast tapings; in May, his trip will include recording three episodes in front of an audience at Symphony Space.

Although he’s not an art world professional, Mr. Tovey has been a passionate collector ever since he earmarked part of his pay from the 2006 film “The History Boys” to buy a print by Ms. Emin, who later became one of Talk Art’s first guests.