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The influencer and animal rights activist, 28, said they "still love each other" and added that the split was down to "family and health issues" and "not anything else", which could imply there were no other people involved.
She said she might get back with the 48-year-old millionaire in the future: "It may not be the end, the end may not be nigh."
Imogen speaking about Kyle split
Imogen and Kyle
Naked except for a fur coat, Imogen said: "We have a lot to deal with separately ... It's probably been one of the hardest years of our lives, separately.
"I've got so much family stuff, and there's so much health stuff involved between us.
"We just kind of want to get each other, get ourselves into the best form of ourselves we can be, without kind of just p**ing in each other's pockets.
"We still love each other very much, we speak every day. We still see each other, we deal with things with each other."
Imogen and Kyle at the ARIAs in 2017
"Everyone's like, 'Is there something else?' But not really," she added.