Question: What were the Royal Navy Battleships, that were considered the first fast battleships and were used in WWI and WWII?

Context paragraphs:
Lion-class battleship: The "Lion"-class battleships were a class of six fast battleships designed for the Royal Navy in the late 1930s.  They were a larger, improved version of the "King George V" class with 16 in guns.  Only two ships were laid down before the Second World War began in September 1939 and a third was ordered during the war, but their construction was suspended shortly afterwards.  Their design changed several times in response to the removal of treaty restrictions on size and in light of war experience.  None of the other ships planned were laid down, although there was a proposal to modify one of the suspended ships into a hybrid battleship/aircraft carrier with two 16-inch gun turrets and a flight deck.  The two ships already begun were scrapped after the end of the war.

List of battlecruisers of Russia: After the end of the Russo-Japanese War of 1905, the Russian Naval General Staff decided that it needed a squadron of fast "armored cruisers" that could use their speed to maneuver into position to engage the head of the enemy's battle line, much as Admiral Tōgō had done during the Battle of Tsushima against the Russian fleet.  This concept was very different from the primary roles for the battlecruiser envisioned by the British Royal Navy and the Imperial German High Seas Fleet, which consisted of scouting for the main battle fleet and attacking enemy reconnaissance forces.  The Royal Navy came to the same conclusion and developed the "Queen Elizabeth"-class fast battleships that could force battle on an enemy fleet and had enough protection to attack any type of ship.  However, World War I and the Russian Civil War interrupted the construction of the Russian "Borodino"-class ships and all were scrapped.

Number 13-class battleship: The "Number 13"-class battleship was a planned class of four fast battleships to be built for the Imperial Japanese Navy (IJN) during the 1920s.  The ships never received any names, being known only as "Numbers 13–16".  They were intended to reinforce Japan's "eight-eight fleet" of eight battleships and eight battlecruisers after the United States announced a major naval construction program in 1919.  The "Number 13" class was designed to be superior to all other existing battleships, planned or building.  After the signing of the Washington Naval Treaty in 1922, they were cancelled in November 1923 before construction could begin.

HMS Warspite (03): HMS "Warspite" was a "Queen Elizabeth"-class battleship built for the Royal Navy during the early 1910s.  Her thirty-year career covered both world wars and took her across the Atlantic, Indian, Arctic and Pacific Oceans.  She participated in the Battle of Jutland during the First World War as part of the Grand Fleet.  Other than that battle, and the inconclusive Action of 19 August, her service during the war generally consisted of routine patrols and training in the North Sea.

G3 battlecruiser: The G3 battlecruisers were a class of battlecruisers planned by the Royal Navy after the end of World War I in response to naval expansion programmes by the United States and Japan.  The four ships of this class would have been larger, faster and more heavily armed than any existing battleship (although several projected foreign ships would be larger).  The G3s have been considered to be proper "fast battleships" since they were well-balanced designs with adequate protection.  Nonetheless the class was officially designated as a "battlecruiser" due to their higher speed and lesser firepower and armour relative to the planned N3 class battleship design.  The G3s carried nine 16 in guns and were expected to achieve 32 knots , while the N3s would carry nine 18 in guns on the same displacement at the expense of a slower speed.

Queen Elizabeth-class battleship: The "Queen Elizabeth"-class battleships were a class of five super-dreadnoughts of the Royal Navy commissioned in 1915–16.  The lead ship was named after Elizabeth I of England.  These battleships were superior in firepower, protection and speed to their Royal Navy predecessors of the "Iron Duke" class as well as preceding German classes such as the "König" class , although the corresponding "Bayern"-class ships were competitive except for being 2 kn slower.  As such, the "Queen Elizabeth"s are generally considered the first fast battleships.

USS Illinois (BB-65): "Illinois" (BB-65) was an uncompleted battleship originally intended to be the first ship of the "Montana" class .  However, the U.S. Navy's experiences in World War II led it to conclude that rather than more battleships larger and more heavily armed than the "Iowa" class , it needed more fast battleships of that class to escort the new "Essex"-class aircraft carrier s being built.  As a result, hull BB-65 was reordered as an "Iowa"-class battleship midway through the war.

Raid on Alexandria (1941): The Raid on Alexandria was carried out on 19 December 1941 by Italian Navy divers of the Decima Flottiglia MAS, who attacked and disabled two Royal Navy battleships in the harbour of Alexandria, Egypt, using manned torpedoes.

HMS Vanguard (23): HMS "Vanguard" was a British fast battleship built during the Second World War and commissioned after the war.  She was the only ship of her class, the biggest and fastest of the Royal Navy's battleships, and the last battleship to be launched in the world.  Work on the ship's design commenced before the war because the Royal Navy anticipated being outnumbered by the combined German and Japanese battleships in the early 1940s.  The British had enough 15 in guns and turrets in storage to allow one ship of a modified "Lion"-class battleship design to be completed faster than the ships of that class that had already been laid down.  Work on "Vanguard" was started and stopped several times during the war and even after construction had begun, her design was revised several times to reflect war experience.  These stoppages and changes prevented her from being completed during the war.

Iowa-class battleship: The "Iowa"-class battleships were a class of six fast battleships ordered by the United States Navy in 1939 and 1940 to escort the Fast Carrier Task Forces that would operate in the Pacific Theater of World War II.  Four were completed, two more were laid down but canceled in August 1945, at war's end, and both hulls were scrapped in 1958.  Like other third-generation American battleships, the "Iowa"s followed the design pattern set forth in the preceding "North Carolina"-class and "South Dakota"-class battleships, which emphasized speed in addition to secondary and anti-aircraft batteries.  Based on wartime experience, they were to serve as fast escorts for "Essex"-class aircraft carrier s.

Supporting paragraphs: HMS Warspite (03) Queen Elizabeth-class battleship
Answer: Queen Elizabeth"-class battleships