In a medium bowl, whisk together the flour, water and salt until smooth. Set aside.
In a small bowl combine the goat cheese, cream cheese, double cream, basil, and spring onion. Mix until smooth. Season with salt and pepper, to taste.
Spoon 1 1/2 to 2 teaspoons filling into each blossom. Close the blossoms and gently twist the petals to seal.
In a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 180°C. (If you don't have a thermometer a cube of bread will brown in about 1 minute.)
Dip the stuffed courgette blossoms in the batter and allow any excess batter to drip off. Fry for 1 to 2 minutes, turning occasionally, until golden brown. Allow the cooked blossoms to drain on paper towels.
Season with salt and serve with your favourite tomato sauce or vinaigrette.