Inside the plug there's a large capacitor with one lead clipped off! Maybe it's a special modification for the UK 240V supply with an under-rated 110V capacitor. The bulk of the nonsensical circuitry is for making the two inverse parallel LEDs light up. (dimly!) Even with the capacitor in circuit the plug would have made no difference to your electricity bill, even allowing for it's shot-in-the-dark "power factor correction".