Great Britain tried very hard for many years to keep the 35.000 ton limit set by the Washington Treaty as long as possible. They committed first to building new ships after the expiration of the building holiday and came up with the King George V class. To get the ships into service at the earliest they went with 14″/356mm guns, the maximum legal caliber in 1937. However international proceedings soon made it clear that more firepower is needed if the Royal Navy wanted to keep their edge. (See more background here on the treaty system etc.)
Already by late 1937, chief constructor Pengelly made it clear that a balanced design with nine 16″/406mm guns would still be possible on a little over 35.000 tons if aviation facilities and a quarter of the secondary battery is surrendered. (The USN was working on it’s second treaty class around this time as well but they went with shortening the citadel to save weight.)
The resulting 16A38 inherited the KGV hull but shifted the tower structure and forward funnel aft due to the larger space required by the two bigger forward barbettes, now both equal in diameter. The forward pair of boilers shifted into the after fire room as well (making the forward funnel slimmer, the after fatter), so no steeply inclined smoke pipes were required. Internal space requirements also dictated this change (less room forward, more room aft due to halved secondary battery magazine space there).
Just as with the US North Carolina class three quadruple 14″ turrets were substituted for the bigger triples as their space requirements appeared to be very close. 14A38 came out 100-150 tons lighter and had the advantage of using mounts and guns already in production.
Estimated power for both designs lay around the 120.000 SHP mark, calculating with forced boilers. This would have allowed a 28 knot top speed deep and clean, or 27 knots if boilers operated normally.
16B-38 essentially duplicated 16A, the only difference was that it used the older, heavier turbines of the KGV class. This added about a 100 tons but saved on cost and construction (design) times.
There was one more design done before the tonnage escalator clause came into effect in late March 1938. 16C-38 brought back aircraft as it was deemed important for scouting duties. Hangars and a cross-deck catapult took up the weight released by the removal of the remaining aft secondary turrets. The resulting ship was cramped and potentially a single hit could disable all secondary armament on one side. Preference was for 16B38, however the displacement escalator clause made any further work on these 35.000 tonners a moot point.