In a frank interview, the model-turned-entrepreneur says their relationship continued after he stepped down as mayor of London and became a cabinet minister – and that they were in touch as recently as July.
Ms Arcuri also comes closer than before to confirming a sexual relationship, saying it is always the woman who is criticised “when you have an affair with an older man”.
Referring to Mr Johnson’s promotion, in July 2016, she said: “He was pissed [off] when he became foreign secretary.
“He could not come to see me because he was followed everywhere [by his security detail]. I was like, 'Just tell them to wait outside. Stop making it seem like I'm some bit. Tell them I am a legitimate businesswoman.”
The revelation that the relationship continued until 2016 is significant because the prime minister has to provide a timeline of his contact with Ms Arcuri.
An inquiry into whether rules were broken because it amounted to a conflict of interest – after she received £126,000 of public money – appears to have been delayed until after the general election, prompting anger.
Ms Arcuri, 34, speaking to The Times, said the pair would recite Shakespeare's Sonnet 29, together “like a weird sense of foreplay”. It begins: “When in disgrace with fortune and men's eyes.”
She revealed she visited Mr Johnson's family home while he was married to his ex-wife, Marina Wheeler, saying: “I admire Marina. I don't know how she put up with it for as long as she did.
“But from my understanding they were two separate people living in a house. Whatever was between them had long gone and it wasn't because of me.
“It wasn't that I was putting him in a position where it's either me or her, because I recognised he had a family, a life.”
The pair met in 2011, when Ms Arcuri says she joked with him that David Cameron, then prime minister, was stealing a march by making technology announcements affecting London.
“I didn't know the extent of the competitiveness between a boy named Boris and a boy named Dave,” she told The Times.
When, in 2012, Mr Johnson asked how they could keep in touch, Ms Arcuri says she said: “Why don't you just call me?" He later sent her a text saying, “Boris calling Jennifer.”
She said: “A friend said, 'You can't have Boris on your phone. Call him Alex the Great.' I didn't even know then his name was Alexander.”
During their first encounter alone, in a hotel bar, he asked her: “Were you a model? You are absolutely beautiful. I can see you being a model and actress.”
She said: "He had complimented me but it was not sleazy in any way,” adding: “I knew where he was going with wanting to pursue me. I am not stupid.
“People had mentioned he wants to sleep with you and I said, 'No, he doesn't. He is just so enthralled with my mind.'”