Preheat oven to 200°C. Cut broccoli and cook in 300ml (1/2 pt) boiling water for 5 to 8 minutes. Drain and reserve cooking liquid.
Cook onion in butter for 5 minutes. Add bacon and chicken and fry. Stir in flour.
Add milk until thick. Stir in reserved cooking liquid, mustard and mushrooms. Simmer for 5 minutes, remove from heat and add broccoli.
For the topping, season flour, rub in butter, stir in 75g (3 oz) of the cheese and all of the milk to form a soft dough.
Turn filling into a 1.8L (3 pt) pie dish. Roll out dough into four 20cm (8 in) squares. Cut each into 4 to make 16 squares. Arrange overlapping on filling. Brush with milk, sprinkle with rest of the Cheddar.
Bake 25 to 30 minutes, until the topping golden brown, and serve hot.