This sounds like a young juvenile swan or a very tame swan that is used to people and was probably looking for food. If it was someone's pet, it may have gotten lost and as looking for its owner. In the U.K., most of the swans are not captive, but are very friendly towards people because they are so used to being fed, especially by young children. So, more than likely, the swan was looking for a handout from your baby as it was used to seeing children and strollers. The Regal Swan