Chop the gammon into 1 cm (½ inch) chunks. Heat the oil in a large heavy-based saucepan, add the chicken, onions and celery and fry gently for 10 minutes, stirring until golden.
Add the gammon, bay leaves, stock and 600 ml (1 pint) water and bring to the boil. Reduce the heat, cover and simmer gently for 40 minutes until the chicken and ham are tender.
Lift out the chicken with a slotted spoon and, when cool enough to handle, shred the flesh from the bones. Return the flesh to the pan with the potatoes and sweetcorn. Simmer, covered, for 20 minutes, until the potatoes are tender.
Make the dumplings. Mix together the cornmeal, flour, baking powder, thyme and seasoning in a bowl until evenly combined. Grate the butter into the mixture and add 250 ml (8 fl oz) water. Mix to a thick paste, adding a little more water if necessary.
Use 2 dessertspoons to roughly pat the paste into 8 rounds and spoon into the soup. Cover and simmer gently for about 10 minutes until the dumplings are light and puffy.