Break the broccoli into small florets and cook in a saucepan of lightly salted boiling water for 3 minutes Drain then plunge into cold water and set one side.
Melt the butter in a saucepan over a medium heat, add the onion, rice and chicken and cook for 5 mins, stirring frequently.
Remove the saucepan from the heat and stir in the flour. Return to the heat and cook for 2 mins, stirring constantly. Stir in the milk and chicken broth, bring to the boil, stirring constantly, then reduce the heat and simmer for 10 minutes.
Drain the broccoli and add to the soup with the sweetcorn and salt and pepper to taste. Simmer for 5 mins or until the rice is tender, then serve.