Unknown Britishism, of uncertain origin.
Maybe from fain, homonym of feign (“to pretend”) and ague (“acute illness”) or cognate French aigüe (as in maladie aiguë, “acute illness”) – literally “to act sick”.
fainaigue (third-person singular simple present fainaigues, present participle fainaiguing, simple past and past participle fainaigued)
- (intransitive) To evade work or shirk responsibility
- (intransitive) To renege in card games