Contest winner Elena Raouna from Doncaster said: “It’s pretty sexist to be honest - I bet he wouldn’t have called me that if I were a man.”
The taunt came when Miss Raouna, 23, tweeted the Apprentice presenter on Sunday evening to say: “Evening sugar ;-) can I call you that? Lol.”
Lord Sugar then replied to say: “Yes no problem as long as I can call you fatty”, leaving a Sugar-free taste in mouths of Miss Raouna’s followers - many of whom are fellow plus size models.
Miss Raouna said: “It’s crazy - it’s all spun out of control. I still haven’t had an apology, it’s just rude to be honest.
“I can’t believe what happened. All I wanted was to send a cheeky message to someone I admired, I used to love The Apprentice but I’m certainly not a fan any more.
“He’s refused to give any comment saying ‘mind your own business’ - excuse me but this is social media and he has 3.8 million followers. There’s nothing ‘mind your own business’ about that!
“Lots of my followers are angry because some of them are plus sized models too, so they might think that’s quite hurtful.
“No one would say fatty to man, I think he should own up and apologise.”