The mA into the base of that transistor is 0.7/10000 = 0.07mA. A typical BC547 has a gain of ~500 so the collector (and LED) current will be ~35mA. It needs a current limiting resistor (~600Ω) and the 10k changing to a lower value (say 2k). That circuit also wastes (0.7/5)% of the power generated = 14%. Also, if you are charging a Lipo battery (which it looks like) then that is very dangerous. Google Lipo charging danger for more info. The solar panel has to generate 3.7+0.7 = 4.4V before any charging takes place and the LED lights.
Mike.