Preheat the oven to 375° and line a baking sheet with parchment paper. In a bowl, whisk the flour with the granulated sugar, baking powder, lemon zest and salt. Using a wooden spoon, stir in the cream and 2 tablespoons of the lemon juice; fold in the candied ginger.
On a lightly floured work surface, gently knead the dough just until it comes together. Pat into a 9-inch round, a scant 1/2 inch thick. Cut the dough into 8 wedges and arrange them 1 inch apart on the prepared baking sheet. Bake the scones for 20 to 25 minutes, until slightly firm and lightly browned on the bottom, pale on top. Let cool for 5 minutes, then transfer to a rack to cool completely.
In a medium bowl, whisk the confectioners' sugar with the remaining 2 tablespoons plus 2 teaspoons of lemon juice until the glaze is smooth. Drizzle the lemon glaze over the scones and let stand for 15 minutes before serving.