How to drive a BC547 using a 0-5V sensor output?
You can do this with a BC547 transistor, but you'll need an op-amp or comparator to amplify the sensor signal first. The transistor won't turn on until you raise the base 0.6 V above the emitter, so for your 0-1 V range, it would be off most of the time. Even above the 0.6 V threshold, the current drive capability of the sensor is very low, so the LED would only weakly turn on.

Once you amplify the sensor signal, you can use the transistor as a digital switch. On this linked page, see the diagram under example #2, labeled Digital Logic Transistor Switch.