Why the Vanguard solution could not become a twelve-ship class

Would Britain have planned more Vanguard-class battleships once Queen Elizabeth-class guns became available?

No. By then the need and viable gun supply would be exhausted, and the 15-inch weapon would no longer be a strong long-term answer to the newest capital ships.

Once Queen Elizabeth-class ships were being retired, the remaining 15-inch gun supply and the strategic need for Vanguards were both running out. The class was better suited to commerce protection and carrier-force roles than to serving as a long-term battle-line response to newer 16- and 18-inch-gun designs. Vanguard made sense because Revenge-class mountings were available while a fast heavy ship still had immediate wartime utility. A notional twelve-ship class would arrive after that opportunity had passed and would compete against purpose-designed counters to Yamato-sized battleships.