Dan was appearing to promote his new political thriller, Gaslit, about former US president Richard Nixon and the 1970s Watergate scandal.
Host Alex Jones addressed Dan about the “extraordinary story”, and asked “what’s the take?”.
Dan replied: “Well, what you’ve got is a criminal for a leader, who is wrapped in a messy war, embroiled in a stupid scandal and surrounded by ambitious idiots, and really should resign… and, erm…”
He then paused, and with faux concern continued: “No, I’m sorry that’s the intro to Boris Johnson.
The comments left Alex and co-host Jermaine Jenas speechless as they quickly tried to move the conversation along.
Speaking to GQ magazine following the appearance, the 39-year-old star said: “It’s hard to ignore the parallels really. And I think with a show, like Gaslit, you know, especially in this country, and people might wonder, ‘well, this is a very American story. I’m not sure if there’s anything that for me.’
“It’s like, well, actually, a scandal’s a scandal, corruption in a political administration is universally relevant, and it doesn’t matter what country you’re in.
“There’s already some, there’s always somebody up to some shady shit. It’s very much headline news here. I hadn’t really realised until I got on the ground. I mean, it’s, it’s one thing to sort of read about it from across the pond.
“But you know, I got here and it’s on every radio bulletin. Absolutely outrageous. And yeah, it got me quite fired up. I thought it was worth highlighting the extraordinary similarities.”
Dan said politicians were now able to get away with things that would have previously led to their resignation.
He added: “I think people need to be held to account and yeah, not a huge amount changes.”
Asked whether the producers had spoken to him after the incident, he aimed a quip at the Culture Secretary.
He said: “And Nadine Dorries storming in trying to privatise me? Yeah. No, I mean, it seemed to go down fairly well. There was massive applause and laughter.
“I think you know, sadly, it’s all too rare to see someone speaking their mind and the truth on live television these days. Even our best political journalists are afraid to actually say what’s going on, which makes me quite cross.”
As a BBC programme, The One Show must follow the broadcaster’s impartiality guidelines.
But Dan added: “There’s impartiality. And then there’s just calling it like it is and just saying what is happening.
“And I don’t think I said anything that should have been any surprise to anyone.”
In Gaslit, Dan plays John Dean, one of the lawyers integral to the case at the time, alongside a star-studded cast including Julia Roberts and Sean Penn.
The criticism follows police fining the Prime Minister and Chancellor Rishi Sunak on Tuesday over a birthday party held for Johnson in No 10 during Covid restrictions in June 2020.
Both Johnson and Sunak – and the Prime Minister’s wife Carrie, who was also fined over the party in the Cabinet Room – apologised on Tuesday and confirmed they had paid the fines.