Combine the peach flesh, sugar and water in a food processor and blitz until very smooth; 1 minute usually. Strain the purée through a sieve into a jug and chill until needed. When you want to make the bellinis, pour 25ml of purée into the base of 4 Champagne flutes.
Top up with the prosecco and garnish the rim of each flute with a slice of tinned peach. Serve immediately with a bar spoon in each glass to help stir the purée if needed.
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