Alexandra, who split from Paul last August after he had an affair, opened up about reconciling with her husband after a "tough year".
"Things are good actually," Alexandra told show host Lorraine Kelly. "I had a wonderful Christmas, a wonderful family Christmas, we really enjoyed it.
"It has been a tough year, it's really hard when you have your life splashed all over the papers, but you've got to get on with it haven't you? You've got to get on with it and make the best of what it is."
Alexandra, who is about to embark on her new career as a TV cook and writer, added that Paul had been very encouraging in her decision.
"He's hugely supportive, in fact he's here today," she said. "He's here to come and hold my hand because it's my first live TV appearance so yes it's going well. I'm really excited about the whole thing. I've got a book on the boil at the moment, too."
Alexandra, 49, who has 12-year-old Joshua with Paul, 47, cooked one of her son's favourite meals on the show, Sinless Southern Chicken, adding that it was a great family dish that "brings the family together".
After Paul's affair with his American Baking Competition co-star Marcela Valladolid, the celebrity chef admitted that it was the "biggest mistake" of his life.
"I did have an affair in America with my co-judge and it was the biggest mistake of my life because actually I still love my wife," Paul told Radio 5 Live 's Richard Bacon.
"We are talking, we are working to get back together again but it's going to take time," he added.