Preheat the oven to 375°F (190°C) and line a muffin tin with paper liners or lightly grease it with non-stick spray.
In a large mixing bowl, sift together the all-purpose flour, baking powder, baking soda, and salt. Whisk to combine and set aside.
In a separate bowl, whisk the eggs until well beaten, then add the sugar, vegetable oil, lemon zest, and lemon juice. Whisk until smooth and fragrant—this creates a balanced, slightly tangy base.
Pour the wet ingredients into the dry mixture and gently fold with a spatula until just combined. Be careful not to overmix—the batter should be slightly lumpy.
Gently fold in the blackberries and poppy seeds, just until evenly distributed. The berries may release some juice, which will add flavor and color to the batter.
Divide the batter evenly among the muffin cups, filling each about three-quarters full. The batter will be thick but scoopable.
Bake the muffins in the preheated oven for 20-22 minutes, or until the tops are golden and a toothpick inserted in the center comes out clean.
Remove the muffins from the oven and allow them to cool in the tin for a few minutes before transferring to a wire rack. The edges should be slightly crisp, while the centers remain moist and tender.
Once cooled slightly, serve these muffins warm or at room temperature, enjoying the combination of zingy lemon and juicy blackberry pockets.