The pair were reported to be seeing one another after Essex was quoted as saying they were an item.
Speaking to Digital Spy and others at The Sun Military Awards tonight (December 11), Willerton claimed there had been "a little bit of a mix-up" with the confirmation.
She continued: "No, I don't know where this has come from.
"We went to McDonald's after the wrap party and apparently that was our first date, but my dad was with us and we went through drive-through."
The model added: "Me and Joey came out at the same time and we've been on lockdown together for the last few days so we've been having an absolute ball.
"We are just friends, but we are very, very close."
Willerton also spoke her jungle experience, adding: "It's completely changed my life. I went into the jungle fairly unknown, now suddenly everybody wants to know what I'm up to. I just feel so lucky that I had the opportunity to go in there and show people who I am."
View all of today's best celebrity pictures: