According to the News of the World, the model's dad Kenneth Parsons wasn't pleased with the couple's weddings plans.
Parsons, who died of cancer last November, reportedly wanted the Strictly Come Dancing star to return to her ex-boyfriend Jason Statham.
"Kelly wanted to bring the wedding forward but Ken wasn't having it," said a source. "He was sure she was making a big mistake.
"Right up until the end, Ken's dying wish was that she wouldn't spend the rest of her life with Billy. He told her that before he died.
"The truth is that Ken didn't get on with Billy from the very start. He always adored Jason. He saw him a kindred spirit and treated him like his own son, like one of the family."
Brook ended her four-year relationship with Zane last week and turned up to the BAFTAs without her engagement ring.