IOTL
5 Queen Elisabeths were ordered in the 1912-13 Estimates
5 Revenges were ordered in the 1913-14 Estimates
3 Revenges were ordered in the 1914-15 Estimates, plus a 6th Queen Elisabeth.
But when Fisher returned to the Admiralty he had the 1914-15 ships cancelled and replaced with the 2 Repulse class and the 3 follies were built in place of the 1914 ships.
Then we get the Hood class which IIRC were originally Super Queen Elisabeth class fast battleships.
The Washington Treaty allowed the British Empire to keep Hood, 2 Repulse class, 5 Revenge class, 5 Queen Elizabeth class, 4 Iron Duke class, the Tiger and built Nelson and Rodney, making a grand total of 20 capital ships.
What I would have done
5 Queen Elisabeths were ordered in the 1913-13 Estimates
5 Queen Elisabeths were ordered in the 1913-14 Estimates
4 Queen Elisabeths were ordered in the 1914-15 Estimates
The 4 ships in the 1914-15 Estimates were completed and another 2 ordered in the War Emergency Programme, making a grand total of 16 Queen Elisabeth class fast battleships.
All 16 were built with oil fired, small tube boilers. However, the weight saved was used to increase their maximum speed to the specified 25 knots. The rest of the saved weight was used to increase the weight of armour, which was arranged on the all-or-nothing principle.
Instead of the Hood class the Royal Navy would order 4 repeat Queen Elisabeths because they were a proven design that could be built quickly than a new ones. Or they would be fast battleships mounting twelve 15" in four triple turrets and a speed of 25 knots. The standard displacement of the new ships would be 32,000 to 35,000 tons.
The smaller displacement compared to the real Hood class means that it will be easier when negotiating The Washington Treaty. The British Empire is allowed to keep the 4 Hoods and all 16 Queen Elisabeth class. Iron Duke is kept as a gunnery training ship and one of her sisters becomes the radio controlled target ship in place of Centurion. Nelson and Rodney are not built. The £15 million saved is spent on new aircraft carriers or on mid-life refits for the Queen Elisabeth class.
This also means that the knock-on effects on the other navies are minimal. As the British Empire has 4 post-Jutland ships instead of 3 the United States might demand that the 4th Colorado has to be completed, turning the "Big Five" into the "Big Six," but there would be no change to the French, Italians or Japanese.
IOTL there Royal Navy's capital ship organisation had by the late 1930s evolved into the Battle Cruiser Squadron (BCS), 1st Battle Squadron (1BS) in control of the Mediterranean Fleet's battleships, the 2nd Battle Squadron (2BS) for the Atlantic Fleet's battleships and the 3rd (Boys Training) Battle Squadron (3BS), which consisted of the 4 Iron Dukes.
ITTL there would be 4 battle squadrons, one of which would be the boys training squadron and each would nominally consist of 4 ships for a total of 16 in commission and the other 4 undergoing long refits or in reserve.
All other things being equal the 5 oldest ships are scrapped under the 1930 London Treaty. However, even if built to the standard of OTL they would be much better ships than the 4 Iron Dukes and Tiger, which were sacrificed IOTL, so the Admiralty would be more reluctant to give them up. Therefore the second London Treaty still extends the battleship building holiday to the end of 1936, but the capital ships that were scrapped by all nations under the OTL treaty could be retained. Therefore the ships that form the Boys Training Squadron ITTL are put into reserve in 1930, rather than being scrapped. They are brought back into service after 1936 as part of the rearmament programme.
IOTL the 5 Queen Elisabeths (and IIRC the 2 Renowns) had refits in the 1920s costing £1 million each. Then in the 1930s, Queen Elisabeth, Renown, Valiant and Warspite had refits costing about £3 million each. Malaya and Repulse had less extensive refits costing about £1 million each. However, ITTL all 16-20 ships have more armour which was arranged on the all-or-nothing system. Therefore cheaper and therefore less expensive modernisations might be needed.
Therefore the modernisation of TTL might involve replacing the machinery which was wearing out, giving the 15" guns greater elevation and a fitting a new superstructure. The completed ships might look like Warspite after her 1934-37 refit. I'd like to see the 16 oldest ships brought up to that standard by 1937. Then the 4 ships that took the place of Hood, Nelson and Rodney would be modernised 1936-40 instead of Queen Elisabeth, Renown and Valiant. Their refit would also see their secondary armament replaced by twenty 4.5" in ten twin turrets.
Although my refit might cost less than Warspite's refit IOTL and £15 million was available because Nelson and Rodney weren't built it is still going to involve the spending of more money to have 16 ships modernised by the end of 1937. Similarly 4 Hood class modernisations 1936-40 are going to cost more than the 3 capital ships that were modernised then IOTL.