Place the gelatine sheets into a bowl and cover with cold water.
Meanwhile, pour 150ml/5fl oz of the champagne into a pan with the lemon juice and sugar and heat gently, stirring frequently to dissolve the sugar.
Remove the gelatine from the cold water, squeezing out any excess water, then add to the pan and whisk until dissolved. Pass the mixture through a sieve into a bowl and allow to cool slightly.
Add the remaining champagne and the basil to the mixture and stir. Leave until the jelly is cold and just on the point of setting.
To serve, divide the chopped peaches equally among eight champagne flutes and carefully pour in the setting jelly. Top each jelly with a sprig of fresh basil and a strawberry.