The scenario here is that the British left is stronger and more radical compared to OTL, and sometime in the 1880s or 1890s they end up launching their own French-style revolution, guillotining enemies of the people in Trafalgar Square and doing all the other things that revolutionaries generally do. The Royal Family manages to escape, fleeing (initially) to France and vowing to return some day and crush the rebels. My main question is, how would the British Empire, and especially the self-governing Dominions, react to such a series of events?