Next, on Radio 4-letter-word, we'll be interviewing Jeremy ...

It is such an obvious trap that you would think that any professional broadcaster would be able to steer around it, but yesterday two of the BBC's most experienced presenters fell right in.

Disaster No 1 occurred just before 8am on Radio 4's flagship programme, Today, as its anchorman, Jim Naughtie, read out a routine announcement about what was coming later in the programme. In the process, he created what will surely be remembered as the funniest broadcasting blooper of 2010, with the original slip-up enriched by Naughtie's valiant but doomed efforts to keep talking without laughing.

What he meant to say was: "First up, after the news, we're going to be talking to Jeremy Hunt, the Culture Secretary ..." But somehow, the hard "C" in "Culture" slipped forward and attached itself to the front of the minister's surname. Mr Naughtie instantly corrected himself, but a second or two later, the import of what he had said hit him and he involuntarily snorted with laughter, and then tried to disguise the noise as a cough.

Then suddenly the airwaves went silent. Naughtie was supposed to announce the time and read the headlines, but he was in no state to do so, and no one came to his rescue. With no choice but to struggle on, his attempts to disguise his laughter weakened with each phrase he uttered.

His co-presenter, Evan Davis, handled the interview with Jeremy Hunt, on the introduction of broadband. Naughtie came back on air after 20 minutes, having got a grip on himself, and apologised for the slip that he blamed on "a certain Dr Spooner" – a reference to a Victorian don renowned for unintentionally switching the first letters or syllables of words.

Naughtie added: "Some of you thought it was funny, some of you were frankly offended. All I can say is that occasionally, in live broadcasting, these things happen and I am very sorry to anybody who thought it wasn't what they wanted to hear over breakfast. Needless to say, neither did I."

Disaster No 2 followed a little over an hour later, during Radio 4's Start the Week programme, hosted by Andrew Marr, who discussed Naughtie's Freudian slip with his studio guests. "We're not going to repeat in quite the terms it happened," Marr promised – and then went ahead and did exactly what he had said he would not do. He immediately corrected himself and apologised, saying: "It's very hard to talk about it without saying it."

As if to make it a treble, the Home Office minister Nick Herbert let slip the same word in the Commons that afternoon when he meant to say "cut".

Some BBC listeners were very offended. Among the comments left on the Daily Mail website was a message complaining that the word the broadcasters had uttered "has got to be the vilest, most revolting of the swear words available to people with no more intelligence than to need them ..." Another complainant wrote: "I'm 88 years old, and when I heard Mr Naughtie's naughty language on Radio 4 this morning I nearly vomited..."

But these were minority views, even among those who contacted the Daily Mail. Mr Hunt was one of the majority who saw the funny side. He tweeted: "They say prepare for anything before going on Today but that took the biscuit ... I was laughing as much as u Jim or shld I say Dr Spooner."

Naughtie's discomfiture is not the only example of someone "corpsing" on Radio 4. The much-respected news reader Charlotte Green lost control of herself in March 2008, when she was supposed to be reading an obituary. No one listening could tell what the joke was. The previous item had been about the oldest recording ever, and someone had whispered in her ear that it sounded like a bee buzzing around inside a bottle.

The word Naughtie used has slipped out on other occasions. When Sir Robin Day was interviewing the Labour MP Dennis Skinner in the 1970s, he tried to say that the MP was a "cult" figure on the left, and mispronounced "cult".

James Naughtie: At 7.59am on Radio 4's Today programme, Naughtie trailed an interview with Culture Secretary Jeremy Hunt by saying: "First up after the news, we're going to be talking to Jeremy Cunt." He quickly corrected himself before struggling to suppress laughter.

Jeremy Hunt: Reacting to Naughtie's unfortunate error, Mr Hunt, the Culture Secretary, tweeted at 8:51am: "They say prepare for anything before going on Today, but that took the biscuit ... I was laughing as much as u Jim, or shld I say Dr Spooner [sic]."

Andrew Marr: At just after 9.30am, on his show, Start the Week, Marr turned to the subject of Freudian slips. Mentioning Naughtie's earlier mishap, he said: "We're not going to repeat in quite the terms it happened." But within seconds he made the same mistake himself.