personally speaking, i'd like a republic because QE2, Anne and Wills aside, i don't much care for the Royals, i'm sick of Philip's stupid bigoted comments and if we were to seize her lands, assets and properties we wouldn't be in debt up to our eyeballs nationally.
societally, it's probably a thing for British dystopias to do away with the Royals because it's an easy, obvious change to make. Ooo, everything's gone wrong because we kicked the Royals out. like, i dunno, adding states to America or having the South win the Civil War for Yanks is a big deal.
as for British society... well... some say we're on the verge of going totalitarian as it is, but that's BS. we only put up with Tory incompetence for 18 years, we'd never put up with a dictator for long.