Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper or lightly grease the baking sheet.
In a medium bowl mix the flour, sugar, baking powder, and salt.
Cut the butter into 4 cubes and add to the flour mixture. Using a pastry blender or fork cut the butter into the flour until the size of small peas.
Toss in the chopped strawberries. In a small bowl beat the egg, cream, and lemon zest.
Make a well in the middle of the dry ingredients. Pour in the liquid and combine until the dry ingredients are moistened.
Turn out the dough onto a lightly floured working surface and knead once or twice. Pat the dough into an 8-inch round circle.
Cut into 8 wedges. Place on the prepared baking sheet.
Place the baking sheet in the oven and bake the scones for 12 to 14 minutes. The scones should be lightly browned.
Remove from the oven and cool on a cooling rack until the scones are cooled.
Prepare the icing while the scones are cooling. Add powdered sugar to a medium bowl add one tablespoon of the lemon juice and mix in. Gradually add enough of the second tablespoon to get the right consistency for drizzling over the scones.