In the interview, the duke denied Ms Giuffre's claims and said an alleged encounter with her in 2001 did not happen as he spent the day with his daughter, Princess Beatrice, taking her to Pizza Express in Woking for a party.
In a clip from the programme released on Twitter, Ms Giuffre says: "It was a really scary time in my life".
"He knows what happened, I know what happened and there's only one of us telling the truth".
Mrs Giuffre has previously claimed she was trafficked to the United Kingdom to meet the Duke in 2001 by sex offender Jeffrey Epstein.
Now 36, she said she was a 17-year-old when they first had sex.
And it appears Charles, 71, had a hand in the Queen's decision to ban brother Prince Andrew from any further royal duties in the wake of the Duke of York's past association with American financier and convicted sex offender Jeffrey Epstein, who was found dead in a Manhattan jail cell in August awaiting trial on new sex trafficking charges involving minors.
Buckingham Palace is bracing for a fresh round of painful headlines following the Prince Andrew saga, as Scotland Yard confirms it is working with the Federal Bureau of Investigation and an explosive television interview is set to air.
After 67 years on the throne and witnessing some of the biggest events of the last century, Queen Elizabeth II is reportedly getting ready to take her most significant step back since her reign began.
As the story dominated British news for a week, overshadowing campaigning for the December 12 election, there has been widespread criticism of Andrew and demands he should answer questions from USA authorities about Epstein.
Commander Murray said that "our position remains unchanged".
She says the force failed to check her allegation that she had been trafficked to London in 2001 by Epstein.
"The MPS always takes any allegations concerning sexual exploitation seriously".
The Met confirmed on Thursday that they had indeed launched the probe, interviewed Guiffe, got the advice from the Crown Prosecution Service, and decided the case was out of their jurisdiction to proceed with a full criminal investigation.
In July 2015, Ms Giuffre went to the Metropolitan Police with her claims, but was ultimately turned away.
"Following the legal advice, it was clear that any investigation into human trafficking would be largely focused on activities and relationships outside the UK".
The Met reviewed that decision in August after Epstein took his own life in USA custody while he was awaiting trial on sex trafficking charges. The alleged incident which is said to have occurred on June 30, 2000, was a security breach as the woman was not searched and did not sign in when entering the royal palace.