The segment started with Stephen’s character waiting to receive a call from the Duke of Cambridge, who seemingly struggled to master the art of Zoom video-calling.
After the initial small talk, the pair discussed the challenges of living in isolation, with William joking about not being able to watch the British soap EastEnders.
Stephen suggested Netflix’s Tiger King as a substitute program, before William quipped he chooses to "avoid shows about royalty”.
The segment concluded with Stephen notifying the prince of his “one-minute call”, at which point William joined Kate and the kids on their front doorstep to “Clap for Carers”.
The Cambridges rare joint TV appearance comes after the family spent the day celebrating Prince Louis' second birthday on Wednesday.
To mark the occasion, Kate and William took to Instagram to share several candid snaps of the prince taking part in a craft project to support healthcare workers.
"Sharing a sneak peek of Prince Louis’s handiwork ahead of his second birthday!” Kate captioned the snaps, which showed the prince with rainbow paint on his hands.
Among the cute snaps was one that shows the cheeky little prince grinning for the camera while wearing a spotless blue gingham shirt.
A follow-up photo shows the prince giggling while showing off his rainbow-coloured hands, while another pic shows his brightly painted handiwork.
Prince Louis and his siblings, Prince George, six, and Princess Charlotte, four, are currently isolating at their country home, Anmer Hall, in Norfolk.