"It's high-end prostitution - it's just scary to think if they've messaged me, they've probably sent it to thousands of pretty girls on Instagram," says Tyne-Lexy Clarson.
She says she was only 19 when she was first propositioned, with an offer of £20,000 for dinner and drinks.
But after starring in series two of Love Island, an agency emailed, offering her £50,000 for five nights in Dubai. It contained a non-disclosure agreement, stating that the details of what she would be required to do would remain confidential.
Tyne-Lexy says she refused the offer, but fears that struggling influencers who do not receive luxury items for free would feel pressure to "keep up appearances" and become vulnerable to these kinds of transactions.
"It's a lot of money for some people, it's life-changing amounts of money."
Rosie Williams, who starred in series three of Love Island, says she was offered £100,000 a year plus all her clothes and bags, to become a companion to a man in Dubai.
She showed us one of the recent messages she had received, from a man purporting to be in Dubai. It says she may be surprised to hear from him but he has an "important transaction" he wishes to share - which she says is a common turn of phrase in these messages.
And she says she would never be tempted, despite the large amount of money involved.
Rosie says it is not an aspect of fame she anticipated: "You're warned about trolling, you're warned that your life with change dramatically, but you're never warned that you could get bought by men."
And she says it is not spoken about in influencer circles: "We either aren't in a position where we need to do it so we don't speak about it, or we've done it and we're too ashamed."
'Degraded and violated'
This programme has seen several messages which influencers have received. The approaches vary from men directly suggesting sex, to agents acting on behalf of a wealthy client.
We received anonymous written evidence from a person claiming to be a British reality star, who said she had been offered £10,000 for sex as part of a holiday package.
"Isabel" said she was first approached on Instagram by a man 10 years older than her, after she had competed in a TV talent show.
"I was initially offered designer handbags. He had a fetish for being financially dominant so he would get a sexual kick out of spending hundreds and hundreds of pounds on bags for me," she explained. "I would also struggle to keep my followers engaged online. So I guess that's why I accepted the offer. "
She said they did not meet for 18 months and spoke every day, so she was excited to meet him.
"He was really pleasant when I was there. At dinner we started drinking and he was asking about my finances - I explained I was in £5,000 of debt. He said: 'Have sex with me and I'll give you double that'."
"Isabel" said she went up to his hotel room and went through with it. "I felt a kind of a mixture of degraded, really annoyed at myself, violated."
But she insists it is not a form of prostitution: "It is a targeted relationship that progresses over time... Whereas I think prostitution is when you agree a fee with a stranger."
The feminist group, Object, which campaigns against the sexual objectification of women, said it understood why women accepted the "hugely tempting" offers.
Heather Brunskell-Evans said: "The women who are involved with this will not want to hear the word prostitution. The reality is that they are selling their bodies for money.
"The groomers are offering the woman everything she needs to be a success at her job as an influencer, but ultimately it's exploitation, and that woman will have to do things for that money that she doesn't want to associate herself with, that make her feel shamed."
Celebrity agent Rob Cooper said it was not only women who were approached. He said one man who was posting online was regularly offered money to perform sex acts.
"I would say a high-level influencer or reality star receives these messages every single day."
He added that social media platforms should find a way of making people accountable to their account - using something like a passport or national insurance number - so that if they're blocked they would have to appeal to get their account reinstated.
A Facebook company spokesman said: "Sexual solicitation is not tolerated on Instagram, and those who repeatedly break our guidelines will be banned. We want Instagram to be a safe space for people to express themselves. We invest heavily in tools and technologies to prevent harassment on the platform."