Catherine, Duchess of Cambridge
03/05/2013 AT 10:00 AM EST
The wait finally ended for more than 1,000 cheering fans Tuesday, as the Duchess of Cambridge
, wearing a brown coat by Hobbs, stepped out in fog-bound Grimsby, a fishing port 180 miles north of London – some 80 minutes late after the clouds held up her helicopter.
As the mother-to-be, 31, was greeted by dignitaries at the National Heritage Fishing Center, an impatient crowd cried out, "We want Kate."
Turning around, the Duchess obliged them with a wave before continuing with her duties.
But the fans also were not shy about remarking on her condition. Bobbie Brown, 42, asked her if the baby had been moving, and Kate responded, "Yes, it is. Very much so."
"She's beautiful, much better than in the pictures," said Dorothy Garland, 74, who had waited about three hours for a glimpse. "She looks so well."
Inside the Fishing Center, which is a museum, Kate had a surprise meeting with a woman who had been shopping on London's Oxford Street last week
at the same time as the Duchess – and had shared a smile with her.
Linda Mitchell, wife of a local Member of Parliament, told PEOPLE, "I said to her, 'We met in TopShop last Wednesday,' and she said yes. I asked her if she bought anything, and she said, 'A few bits.' I told her I was going to say 'hello' but that would have been difficult. She said it would have been wonderful."
After the museum, Kate's "away day" (as the royal staff call it), also included making her very first visit to see some of the work done by the Prince's Trust – the children's charity set up by her father-in-law Prince Charles to help disadvantaged youngsters seek work, training and education.
At the Peaks Lane Fire Station, Kate was due to see a 12-week personal development plan that helps those between the ages of 16 and 25 find the skills and confidence to get hired.
Later, she will officially open a new building at the Havelock Academy, a high school with 1,000 students in one of the most socially and economically challenged regions in the country.
As she left, Kate thanked staff for their tour, saying, "I've really enjoyed myself. It was a wonderful experience, so authentic – especially the smells and the noises."