The Democrat was due to speak about why she lost the 2016 US presidential election to Republican Donald Trump.
Presenter Jane Garvey apologised to listeners close to the programme’s end, saying: “Hillary Clinton has been delayed this morning, as I’ve already said … she’s not going to make it before the end of the programme. I’m really, really sorry about that. I think you probably understand just how sorry I am.
“But we are working very, very hard to get this interview rescheduled and Hillary Clinton is very apologetic.
“So what can I say, that’s the situation.”
It follows a string of late arrivals by the former US secretary of state over the weekend.
Mrs Clinton was about 45 minutes late for a speech at the Cheltenham Literature Festival on Sunday to promote her new book, What Happened.
She was also delayed a similar amount of time on Saturday, when she was presented with an honorary doctorate at Swansea University.
Meanwhile, her husband Bill was forced to postpone a planned intervention in Northern Ireland’s political stalemate because of storm Ophelia.
The former US president had been due in the region today to meet warring political parties as they continue to struggle to reach a deal to restore the collapsed executive.
But the visit was called off at late notice due to the severe weather warnings. It is understood the visit may still take place on Tuesday.
Yesterday Mrs Clinton appeared on BBC One’s Andrew Marr Show where she was challenged on her Brexit opinions.
She said: “I wanted to make another point about Brexit. Looking at the Brexit vote now, it was a precursor, to some extent, to what happened to us in the United States.
“But the amount of fabricated, false information that your voters were given by the Leave campaign…”
But Marr was keen to put the American in her place, pointing out Brexit campaigners were not the only guilty party in this suggestion.
Marr said: “From both sides, I must say here.”
Mrs Clinton stumbled and replied: “Well, I’m not as familiar with… But, I’m very familiar with what the Leave side said because they transported a lot of that on behalf of Trump.”