Latifa's father, Sheikh Mohammed bin Rashid Al-Maktoum, is vice president and prime minister of the United Arab Emirates, of which Dubai is a constituent.
"I don't want to be a hostage in this jail-villa - I just want to be free". She talks about not knowing what her fate will be and about being exhausted of living in that place.
The videos are to be shown on Tuesday evening on the BBC's "Panorama" broadcast, which they received from close friends of the princess.
In an incendiary ruling previous year, the High Court in London made a ruling of fact that Sheikh Maktoum, 71, had "ordered and orchestrated" both occasions on which the princess has been kidnapped and held against her will.
This is not the first time the ruler of Dubai faces accusations of family abuse.
The damning High Court ruling followed a protracted bitter child custody battle between Sheikh Mohammed Bin Rashid Al Maktoum's and his youngest wife, Princess Haya.
Days later, when she had got as far as India's Malabar coast, Indian - then Emirati - forces violently boarded her boat and returned her to Dubai.
Those who had managed to contact the princess say they are now anxious for her well-being after the messages, sent after her kidnapping in March 2018, suddenly stopped.
"All the windows are barred shut, I can't open any window".
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Panorama identifies the friends who have provided the videos as her maternal cousin Marcus Essabri, Tiina Jauhiainen, the Finnish coach who accompanied her in his escape, and activist David Haigh.
The BBC said the authorities in Dubai and the UAE had failed to respond to requests to comment on the princess's current condition.
Ms Robinson, a former UN High Commissioner for Human Rights, has joined in calls for immediate worldwide action in order to establish Princess Latifa's current condition and whereabouts. She said she was making the video in the bathroom of the villa, the only room she could lock herself into.
She told the BBC she now feels she was "horribly tricked" by the princess's family. "Things have moved on, and so I think it should be investigated", she added.
She said she did not ask Latifa about her situation because she did not want to "increase the trauma" of Latifa's "condition".
"This woman is imprisoned and has no permitted contact with the world", Kenneth Roth, executive director of Human Rights Watch, told the BBC.
In 2019, the tensions within Dubai's ruling family were laid bare before England's High Court after one of the sheikh's wives, Princess Haya, fled to the United Kingdom with two of her children and applied for a protection order and non-molestation order against the sheikh. "The police threatened me that I would be in prison my whole life and I'll never see the sun again".