1) The "10 cm Plastic wire" is confusing, what should be used is an isolated wire so that it is IMPOSSIBLE to make (conductive) contact to anything and especially mains voltages (220 VAC).
2) this circuit actually work on capacitive coupling between 220 VAC, that "Antenna" and also capacitive coupling between you (your hand) holding the circuit. This capacitive coupling causes small AC currents to flow and the circuit detects those.
3) To improve sensitivity, you could increase the capacitive coupling. This can be done by not using a wire as the antenna but a small metal plate of 2 x 2 cm for example and mounted at the inside of a plastic box. Like the wire it needs to be isolated so the plastic box is needed. Then also place a second metal plate (or something else conductive) inside the box on the side that will be closest to your hand.
So: it is important to remember that the circuit including everything connected to it should be inside a plastic box. That's the only way to make it safe to use to detect 220 V AC. If you ignore this advice, you're risking your life!
Last remark: this is a simple circuit, I believe it can work provided there is enough capacitive coupling to the 220 V AC. But you might not be able to reach the 5 cm, for that you might need a more advanced design.