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Prepare two days in advance: dissolve the sugar in a pan with 300ml/1⁄2 pint water over a low heat. Put the lemon balm and bay leaves in a bowl. Pour in the hot syrup and lime juice, cover and leave in a cool place for at least 2 days.
Several hours ahead, have ready a bowl of iced water. Plunge the peaches one at a time into a saucepan of boiling water. Remove from the pan immediately and put in iced water.
Peel the peaches, then cut them in half and remove the stones. Put the halves in a bowl and strain the syrup over. Cover and chill for about 2 hours, basting from time to time.
To serve, spoon a peach and some syrup into each dessert glass and serve with clotted cream and Balmoral biscuits on the side.
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