Its been a long time since I worked with an LM358 and I don't recall the actual minimum output voltage. However I'm pretty sure the output being a PNP will not go much below 0.8 Volts. This level can turn on your BC547.
You could:
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add a diode or two in series with the LM358 output.
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add a resistor from the base of the BC547 to ground, perhaps 5k or so.