Mark said he was forced to speak up after finding it "embarrassing" that Lauren regularly spoke about him and Michelle in her weekly magazine column. In a series of tweets, the 28-year-old urged his former fiancée to respect his wife and stop talking about their relationship in public.
He wrote: "Endless mentions RE: me and us is embarrassing. I really thought after lawyers being involved and polite pleas to stop mentioning me she would stop.
"Maybe not. It's hurtful to think one person needs to mention YOU every week to earn a living. Being married to another women almost makes it unfair!! If your reading this, please PLEASE respect my wife and STOP.
"Everyone has a past, get over it!! I really didn't want to have to do this but enough is enough. I wish you well but leave me, my life and my wife out of it. I'm sure there is other ways to make money."
The television presenter also retweeted messages of support from fans, telling one that he "had to speak up" about the issue despite still being away on his honeymoon.
Mark's tweets follow Lauren's recent magazine column, in which she wrote that she "felt sorry" for the couple, because "no-one wants their ex mentioned on their wedding day".
Lauren has not replied to Mark or addressed the matter on social media. In recent days she has been sharing a series of holiday snaps from her holiday in Dubai – the same place that Mark and Michelle are currently honeymooning.
The dispute has not stopped Mark and Michelle from enjoying the final days of their honeymoon. The loved-up pair have been sharing pictures from the trip on social media, with Mark revealing that his family had joined in on the fun.
"What a ride yesterday!! When the family joined the last couple of days of the honeymoon fun!! #lovedit," Mark captioned a video of the group on a water ride.