What is their purpose ?

Mostly used as a suppressor for medium wave radio to cut down interference on the likes of alternator, wiper motor etc. the lead coming out is the +ve end and the bolt on bit negative
You can probably remove if you dont use the MW band on the radio
Source: The Rolls Royce Forum - England

How to test ?
To test a capacitor, set the multimeter to resistance and connect up capacitor to it observing polarity, the meter should shoot up in resistance then drop back to zero, maybe you will have to use an old fashioned analogue test meter.
Source: The Rolls Royce Forum - England