I've done as you suggest but I can only get a reading part-way along the track. However I've measured the current across the output at 2.5A. The output for the charger is rated at 200-240mA so can we come up with a suitable value from that info?
Oh no, you didn't just put the meter on the current setting and stick it across the output did you? In that case you've measured the short circuit current, not the charging current. You're lucky the internal resistance was high enough to limit the current otherwise it would've blown the fuse inside your meter.
If it's just a rectifier and transformer type of charger, the more sensible approach is to measure the open circuit voltage, then work out the required resistor value to put 240mA into a discharged battery.