By the mid-sixteenth century kings in England weren't really building themselves castles anymore (The English rulers in the mid-16th century were Henry VIII, Edward VI, Mary, and Elizabeth I). After gunpowder was developed, large guns (ie canon) that could pierce castle walls made medieval siege warfare largely impractical. Kings and other nobility started living in buildings that we are more likely to call palaces, mansions, manor houses, etc. What the English often call "Stately Homes." At the same time, militaries began building forts to house soldiers and supplies separate from where the nobility were living.

If you're interested in an overview of medieval castle construction, I'd actually recommend David Macaulay's Castle. It's a children's book, which is not the normal thing recommended on Ask Historians for sure, but it was written and illustrated by an architect who did a lot of research into castle construction.

There's also a Dover Thrift book called Castles: Their Construction and History by Sidney Toy.

From 1378 the English Crown maintained a government department called the Office of Works. This was a full service construction organisation employing master craftsmen, designers, artists, and labour, transport, and materials specialists. The Office would build anything that the king needed building, castles, palaces, monasteries, colleges, churches, fortifications, it also maintained existing buildings, kept an extensive design archive and consulted for other patrons. Full information on this can be found in the multi volume official 'History of the King's Works' published by Her Majesty's Stationery Office (the UK government publisher). In the 16th century, the king would summon the head of the Office, say what he wanted, designs would made and approved then the Office would acquire labour and commence work.