It was revealed earlier this month that the Family Fortunes host, 35, had replied to Sugden and four other women's Twitter and text messages.
Kay is married and has two children with Strictly Come Dancing presenter Tess Daly.
"It was a bit of flirting but nothing ever happened between Vernon and I. He's a good-looking guy but at the end of the day he's married and it would never have gone any further than a bit of flirting because I'm not that sort of girl," Sugden told the Daily Star.
"It's all been blown out of proportion. It's not what everyone thinks. It was just a few flirty texts. If I could turn the clock back and not send or receive those messages then I definitely would do. I regret receiving them from Vernon and I regret replying but it was all just a bit of harmless fun."
She added: "Unfortunately we can't turn the clock back. I just hope that Vernon manages to get his marriage back on track now."