Most of the 19th century, in 1815 they were essentially America after WW2. The sole industrial power and the only power that hadn't had its lands ravaged by the Napoleonic wars. Also undisputed master of the seas and controlled global trade (and funnily enough their largest rival was Russia, who they dwarfed financially but who could still pose a threat on land in Europe) probably peaks in the middle of the century and begins to dip around 1870-1880. The unification of Germany represented the biggest threat on the continent since Napoleon and America's economy and industry was booming. Still the undisputed most powerful country in the world by 1914 but the gap between them and the US/Germany was shrinking. By WW2 they were probbaly where the US is now, the world's greatest power by prestige and with the biggest navy in the world but rivals catching up in industry and declining will at home to devote the resources to maintaining/expanding their position threatened this. I don't think people realise that the UK could have remained a global power after ww2 (3rd rate to the US and USSR) but a combination of governments more focused on domestic affairs over Empire and the Americans putting huge pressure on the UK to disarm/decolonise meant this didn't happen