The fashion designer as we understand the concept was not in evidence during the Elizabethan era. Clothing styles were influenced by the Queen and Elizabeth herself is known as a great influence on fashion. She left detailed records of her sense of style in wardrobe accounts that included information on textiles, where they were bought, and how much they cost. Style followed the monarch, for example, Henry VIII's size and girth led to men wearing large, puffy garments to emulate the king. Elizabeth I was small, small-breasted, and slim so costume for women reflected her figure.
New styles were brought in from other countries. The Spanish farthingale was introduced to England by Katharine of Aragon, the first wife of Henry VIII. During the reign of Elizabeth I, the idea of starching ruffs was introduced by the wife of a Flemish coachman. ( Mrs. Nevill Johnson, May 1903 "The Connoisseur an Illustrated Magazine for Collectors"). When the queen fancied a particular fashion concept, she brought in foreign tailors and dressmakers, or imported garments from other countries.
Clothing styles were also influenced by law. Certain textiles, colors, and garment cuts were mandated by sumtuary law which regulated clothing according to status. For instance, gold and silver embellished garments could only be worn by the royal family. Purple silk could only be worn by the royal family. Law mandated what the nobility could wear. This even extended to birth order.
So the styles worn during the period were influenced by many people including tailors and dressmakers. The concept of the unique fashion designer who was a celebrity in their own right came much later.