Doug Richard, 57, contacted the girl through a "sugar daddy" website last year.
He told the Old Bailey he would never "knowingly have sex with a child".
Mr Richard denies charges of sexual activity with a child, causing a child to engage in sexual activity and paying for sexual services.
He told jurors he had used the website Seeking Arrangements for around four years and had gone on to meet some women in their 20s for sex.
"As mortifying it is to say, I was looking for role play and fantasy relationships involving dominance and submission," he said.
The entrepreneur first messaged the 13-year-old girl after being attracted by her profile, which described her as "submissive".
Mr Richard, of Islington, north London, said he had believed the girl was of legal age.
"You cannot sign up on the site unless you are 18. I just assumed and her profile said 18," he said.
Richard went on to describe meeting the girl and her 15-year-old friend at a cafe before heading off to a pre-booked apartment.
He admitted engaging in various sexual acts, including spanking the girl, but denied she ever appeared to be upset or hurt.
"This is all about role play and fantasy and having fun. If it's not fun I would have stopped," he said.
Mr Richard told the court he gave the two girls Â£120.
"I was trying to be very 'sugar daddy'," he said.
"It was a gift basically. I was trying to be nice so I gave them some money to go shopping."
He told the court the reputation of his business initiative, which brought him into contact with the UK government as an adviser, had been "shattered".
The trial continues.
A former Dragons' Den star accused of paying a 13-year-old girl for sex was "looking for role play", a jury has heard.