Put lemon juice in a small, flat bowl. Put the sugar on a small plate. Dip glasses first upside down into the juice, then into the sugar. Leave to dry. Warm up the blackberry jelly and stir until smooth. Pour into a small measuring cup and stir in gin. Wash thyme and shake dry.
Divide blackberry gin syrup into 12 champagne glasses and put one frozen blackberry in each glass. Fill up with sparkling wine and put a thyme stalk in each glass.