Final answer:
Jahangir, the son of Akbar, permitted the English East India Company to set up trade settlements in India.
Step-by-step explanation:
The Mughal ruler who permitted the English East India Company to set up trade settlements in India was Jahangir. Jahangir ruled from 1605 to 1627 and succeeded Akbar as the Mughal emperor. During his reign, he had established a commercial relationship with the English and allowed them to establish trade settlements in India.