Kongo is still older. But not by much (Warspite would be the third oldest ship now after Kongo and Hiei).
The Queen Elizabeth-class are more or less the first fast battleships, as they are fully armored battleships with heavy guns, but with cruiser speeds (are at least older cruiser's speeds, since she could keep up with many of the older battlecruiser of that time). Kongo is considered the battlecruiser version of the battleship Erin (which was the import Ottoman battleship Reşadiye), which itself was based on the old King George V-class and some improvements that would show in the Iron Duke-class.
Of the major British capital ships used in the war, HMS Revenge was built in the same shipyard as Kongo. So she could be treated like a younger sister (or niece maybe). But also carriers such as HMS Illustrious and HMS Indomitable. Also some late war carrier, but I would doubt they'd be used as they didn't do much in the war (though ex-HMS Hermes, present day Indian aircraft carrier INS Viraat, is still in service.)
Of course Kongo has two elder Japanese batteships built at Vickers: Mikasa and Katori.