The UK was already on the road to universal suffrage, European peace wouldn't require many substantial changes to British history. French revanchism was a key component of the road to war, but France was never powerful enough to start a conflict on its own. The crucial factors come down to democratization, land reform, and development in Germany, Russia, and Austria-Hungary.
Eliminating Magyarization and the Hungarian landed gentry's control over politics in their half of Austria-Hungary would create more of an incentive to industrialize, and give more nationalities a stake in the Empire's continued existence. This would ensure a much more stable Europe and make irredentism by Romania, Serbia, or pan-Slavists in Russia less viable.
If most of the Empire was ruled the way Cisleithania was, the Slavs would have less reason to try and leave the Empire or support a greater Serbia. A smaller linguistic-religious group like the Slovaks, Slovenians, or Galician Ukrainians could realistically obtain equal language rights and representation in a larger Imperial Federation. Without the Empire, the most likely alternative is being a peripheral, forcibly assimilated minority of someone else's Greater_X nation state (Slovenes, Croats under fascist Italian rule and in interwar Yugoslavia), or as the minor client states of Germany and Russia.
If the Russian crackdown on political radicals was much harder and Lenin and Stalin were executed instead of being exiled to Siberia or imprisoned, Europe's 20th century would be much better off. Land reform and gradual moves toward parliamentary rule would head off peasant support for socialism and violent revolutionaries, but democratization wouldn't solve Russia's nationalities question. I'm pretty sure Russians were only a plurality of the Empire in 1914, so it would be very hard to hold everything together.
It's very hard to tell exactly how Germany could become a full democracy without WW1. The contradiction between an increasingly urban, industrial society and a political system dominated by the Kaiser and landed gentry would become larger and larger over time. A reformist Kaiser may willing to play Gorbachev and give up power to the Reichstag and Chancellor, or a crisis over the military budget could lead to the Kaiser's fall. Wilhelm II was too militaristic and autocratic for the Catholics and trade unionists, but not militaristic and autocratic enough for the colonial league and the volkish/antisemitic groups.
A large reactionary faction in East Elbian Germany never really bought in to democracy during the Weimar period, and a democratic German Empire may suffer from the same problem. West Germany managed to democratized successfully because Nazi Germany destroyed the social base of conservative authoritarians who put them in power, and took the Junker establishment with them during their defeat in 1945. The two leading groups in the West Germany, the ex-Zentrum Christian democrats and the SPD, were much more on board with democracy than eastern Germany.
Democratization in eastern Europe without communist rule would be much messier and more gradual, with lots of dealmaking and the occasional backsliding. The church, the monarchy, the aristocracy, and upper middle classes who might've potential nationalization or redistribution by democratically elected soc-dems and socialists would still be around to frustrate moves toward democracy. The military in non-Soviet communist eastern Europe also lacked the independent role enjoyed by armed forces in southern Europe and Latin America.