Much of this is old hat to some of the people I know have already responded but just as general background to the original question -- basically, politics and inertia.
The N3 design had some innovations based on WWI experience in terms of armor and of course the larger guns. Under the new arms control limitations, however, the guns were too big and the total displacement was far too heavy, so the design had to be scrapped. The Nelson class was a compromise intended to fit within the treaty requirements while borrowing some ideas from the N3 work.
The next class after the Nelsons, the new KGV class, was designed in anticipation of another arms control treaty that would have limited the guns to 14 inches.
Japan refused to accept the terms of this treaty. This was anticipated by the negotiators who agreed that in the event, the gun limit would be raised to 16 inches. Britain then went ahead with a new design carrying 16 inch guns and shaving down armor and secondary guns to stay in the weight limit.
However, because Japan also then refused to provide any other information on its new battleship designs, the treaty weight limits were raised to 45,000 tons (IIRC) in 1938. By that time design work on the new British class was already well advanced so they tacked the armor and secondary guns back on. This is the Lion class, which ultimately was never completed.
Then, in 1939, it became clear that new German and Japanese construction -- well beyond treaty limits -- would require a British response, so they moved to another new design, which became one ship, the Vanguard. Rather than an all-new design, though, this was basically just the Lion design but modified to carry an extra turret. (Four turrets total, because the British just happened to have four turrets left over from converting old battlecruisers into aircraft carriers, so it saved them the cost of buying new ones.)
And after Vanguard, of course, it was pretty obvious that the age of the battleship was done and that even if it wasn't Britain wouldn't be leading the battleship race anymore anyways.