How did the British East India Company gain control of much of eastern India?

The British East India Company gained control of most of eastern India by offering protection to kings and Nawabs of the provinces in eastern India in turn for the rights to collect taxes.

Explanation:

Before the British actually declared their control over India, they began with seeking the rights to collect taxes and look over small regions from the then rulers of different provinces in India. The first stated that their intention was to expand trade but they gradually went on tightening their grip on the administration of India.