The Dancing On Ice host claimed that the couple are "incredibly conscious" in front of photographers and wouldn't want to scare their family members with a big celebrity ceremony.
Bleakley told Fabulous: "We're not big flashy types... but we wouldn't be allowed to be anything other than normal, and it's not in our nature. If I got ideas above my station, it would be knocked out of me quickly.
"It'll be a very personal day, so we won't be selling it to a magazine. Absolutely not. Frank and I are both incredibly conscious in front of a camera, and besides anything else, it would be my parents' worst nightmare. My family are so not in this world and it wouldn't be fair on them."
Bleakley also addressed her Christmas time fall out with Lampard's ex-fiancée Elen Rivas over the former couple's daughters, as well as the subsequent reports that Luna, 6, and 4-year-old Isla call her "mum".
"I don't really want to talk about it because you can imagine the drama that would cause," she said. "But no, they don't call me 'mum'. We just have a really lovely relationship and they're such happy little girls."
Bleakley became engaged to Lampard last June.
> Christine Bleakley on Frank Lampard wedding: We will marry when ready