Sorry, wasn't clear enough. The PNP just switches the battery onto the LED when there is a power outage. As to current limiting, I was just thinking of an external board introduced between the battery and LED. Consisting of an NPN, 2 diodes and 2 resistors. I tried this out and it worked quite well. However, a mirror image circuit with A PNP should work just as well. In this case it should be possible to employ the 'switching' PNP to limit current flowing to the LED with the addition of 2 resistors and 2 diodes/1 zener.
So, output from charger is ~125mA through a 'charging' diode to +ve of battery (prevents reverse current flow when power outage occurs).
+ve of battery to emitter of PNP and collector to LED. Cathode of LED to ground. PNP base is connected to other side of 'charging' diode.Modification to this existing arrangement is a resistor (1R5) between PNPemitter and +ve battery. Two diodes in series between +ve battery and PNPbase. These create a set voltage when conducting. Probably better to use a zener (2V4). A resistor (1k) from the other side of the 'charging'diode to PNPbase.
Varying the value of the 1R5 resistor effects the level of current to the LED.