Channel 5's programme claims that the Queen responded to the news from her private secretary by saying: "Someone must have greased the brakes."
Diana: 7 Days That Shook The Windsors will revisit Diana's fatal crash in August 1997, airing comments from "key players" involved in her funeral holding detailed accounts from the time after her death.
The TV show's claims also echo royal biographer Ingrid Seward's report in her 2015 book and article.
According to the Channel 5 episode, Miss Seward wrote in the Daily Mail: "According to one witness present when the Queen heard the initial news, she mused out loud, ‘Someone must have greased the brakes’.
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Someone must have greased the brakes
Diana : 7 Days That Shook The Windsors claim
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"That astonishing remark reveals something of the extraordinary and complex relationship between her and Diana."
Tonight's episode also claims Prince William at the young age of 15 initially refused to join his mother's funeral procession.
In a recent interview with the latest issue of GQ, the royal said: "I still find it difficult now because at the time it was so raw. And it is not like most people's grief because everyone knows about it.
"It's a different situation for most people who lose someone they love. It can be hidden or they can choose if they want to share their story."
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Speaking about his mother not being around today to see his wife and children, he continued: "I would like to have had her advice. I would love her to have met Catherine and to have seen the children grow up. It makes me sad that she won't, that they will never know her."
The Duke of Cambridge added: "I want to bring up my children in a happy, stable, secure world and that is so important to both of us as parents.
"I want George to grow up in a real, living environment. I don't want him growing up behind palace walls. He has to be out there. The media make it harder but I will fight for them to have a normal life."
Diana: 7 Days That Shook The Windsors airs tonight on Channel 5 at 9pm.