switching with transistor
As the BC557 is a PNP according to your figures you have 1.2 - 0.5V (= 0.7V) across the base-emitter junction at turn on which sounds correct. 

You could try adding a schottky diode (anode to base of bc557) to increase the 'base - emitter' drop and reduce the value of the 'turn on' voltage. This will not give you a precise turn on but it will get you closer to your 0.2V.



The forward drop of a schottky diode is about 0.2V. You could also experiment with a couple of germanium diodes (about 0.17V each) or even try a silicon diode (~ 0.65V).