The phrase 'On the Boil' means that if a situation or feeling is on the boil, it is very strong or active.
Example of Use: "The corruption scandal is being kept on the boil by a series of new revelations."
'Boil' comes from the Old French word 'bolir', which originated in the Latin word 'bullire'. Both words means literally to gush, seethe, bubble, or swell in the way water does when it boils. The origin of the idiom 'on the boil' comes from the 1640s, when the term 'boil' was first associated with agitated feelings.