The couple had a private ceremony, with just 17 guests, on a beach in the Seychelles in April.
"Everyone thought I'd want a big thing, but I know when things are meant to be kept private," she told Grazia magazine.
She continued: "I want an album of wedding photos to show my kids, not a magazine.
"I had so many texts from people saying well done for not selling out. There were just 17 of us and it was really relaxed, really lovely."
The 35-year-old presenter says she is enjoying the security of being with someone.
"After our honeymoon in the Maldives, I put on about half a stone," she added.
"I'd gone very soft round the waist. But that's what your wedding and your honeymoon are about - I let myself go, ate everything in sight and drank cocktails at sunset. But that's what it should be. You can't have a wedding and not eat the cake."
The couple aren't making any plans to try for children just yet, Denise says: "It's just too much pressure, we want to enjoy married life."
The full interview appears in Grazia magazine, on sale today (Tuesday).