By cutting off the funding source, you are effectively cutting off the oxygen supply that fuels the fire, which means that it will soon be extinguished.
These insurrections/terrorist campaigns are fueled almost exclusively by money and grievance. Once you have a government-as in the cases of the current Sinhalese government in Colombo, or the current British government at 10 Downing Street-that is willing to address the demands of the aggrieved minority in an honest manner, all you need to do is quell the flow of blood money into the center of the conflict.
I'm sure you know more about it than I, but in Phnom Penh the Tamil arms purchases were fueled by heroin, according to those who were paying attention to it.
$14,000 a kilo for scag, $75 for a good AK, $125 for an M-16, $5 for a hand grenade.