The A Place in the Sun host admitted that her calm persona went out the window when she heard she would have to have the operation.
"I lost it a bit and started to tense up," said Laura. "I've never had an operation in my life. I was rushed into theatre, Alex put on his scrubs and I was given a spinal cord. We were told our baby would be here in three minutes.
"I would have loved to have had a natural birth, but the important thing is that he is fit and healthy," she added.
The couple revealed that they were originally set on the name Ethan, but decided on Rocco after they met a little boy with the same name.
"We're on the same page when it comes to how we look after Rocco," said Laura. "We leave him to cry a bit. We agree on that.
"Alex is as wonderful a father as I expected him to be. He's hands on and had changed more nappies than I had before Rocco's arrival because he has a niece and nephew."
For the full story and more pictures of Laura and her new family, see this week's issue of HELLO! on sale now.