England was primarily ruled by Queen Elizabeth I during Shakespeare's time. She ruled from 1558 until her death in 1603. After that, King James I ruled, known as King James the IV in Scotland.
Shakespeare lived from 1556 to 1616, so it was primarily Elizabeth's rule and patronage that influenced his life, though King James also supported him while he still only ruled Scotland. Both of the them were big patrons of the arts, especially those on the stage. Shakespeare often makes allusions to her in his plays, including a passage grieving her loss in Henry VIII, according to the website Shakespeare Online.