The battle of Plassey (1757 AD) and the battle of Buxar (1764 AD) were decisive in establishing the British control over Bengal and Awadh respectively.

1. Bengal

Misuse of Royal Farman for Trade in Bengal by the British: The English East India Company secured a royal farman in 1717 AD by the Mughal Emperor granting the Company the freedom to export and import goods from and to Bengal without paying taxes and right to issue dastaks (passes) for the movement of such goods. The Company servants were also permitted to trade but were required to pay the same taxes as Indian merchants. This farman was a major cause of tension between the Company and the Nawabs because it fetched less revenue for Bengal. All the Nawabs of Bengal, from Murshid Quli Khan to Alivardi Khan, had been annoyed with the British misuse of the farman. Moreover, the Company’s servants misused the power to issue dastaks for the Company’s goods which caused loss to the royal treasury.

Siraj-ud-Daulah’s Ascendancy to Throne: The hot-tempered Siraj-ud-Daulah who succeeded his grandfather, Alivardi Khan in 1756 AD, asked the Company to trade as per the same rules and regulations as in the times of Murshid Quli Khan. The British refused to comply and levied heavy duty on Indian goods entering Calcutta, which was under their control. This move greatly annoyed the Nawab. The Company was also fortifying Calcutta as part of its preparation for war with the French. The Nawab ordered to demolish their fortifications. The British refused to obey the order of Nawab causing more tension between the Nawab and the British. Consequently, Siraj ud- Daulah invaded Kasimbazar and captured Fort William in Calcutta (present Kolkata) in 1756 AD.

Battle of Plassey: British hatched a conspiracy by which they planned to place Mir Jafar on the throne of Bengal. They first presented a near impossible set of demands which Siraj-ud-Daulah refused to comply with thereby worsening the already tense situation. A battle ensued at Plassey, (20 miles from present Murshidabad) in June 1757 AD. Mir Jafar and Rai Durlabh betrayed the Nawab and sided with the British. Nawab Siraj-ud-Daulah was put to death by Mir Jafar’s son Miran. The British emerged winner in the battle of Plassey.
After their victory, the British proclaimed Mir Jafar as the Nawab of Bengal and got the right to free trade in Bengal, Bihar, and Orissa (now Odisha).  besides a huge sum of money as compensation. Mir Jafar could not meet the demands of the Company. Subsequently in 1760 AD, the British made Mir Qasim, son-in-law of Mir Jafar, the Nawab of Bengal. But he also did not completely bow down to the unreasonable and illegitimate demands of the British and the obvious happened. The British defeated Mir Qasim following a series of battles in 1763 AD.
Furthermore, in order to legitimize its reign in Bengal, the company signed a treaty with the Nawab of Bengal Nizam ud-Daula in 1765 AD and secured the Nizamat of Bengal and from Mughal Emperor Shah Alam II they got the Diwani of Bengal, Bihar, and Orissa.
2. Awadh
Emergence of Awadh as an Independent State: As the Mughal empire declined and lost its control, Awadh grew stronger and more independent. Awadh was important because it controlled the doab, the fertile plain between the Ganges and the Yamuna rivers and had enough wealth to safeguard its independence from the threats of the increasing influence of the English East India Company. The Nawabs of Awadh were a Persian Shia Muslim dynasty from Nishapur. Saadat Khan Burhanul Mulk was appointed the first Nawab of Awadh in 1722 AD who set up his court in Faizabad near Lucknow. His successor was Safdarjung (1737 AD–1754 AD), an influential noble at the Mughal court in Delhi.
British Enmity with Nawab Shuja-ud-Daula: The third Nawab, Shuja-ud-Daula (1754 AD–1775 AD) broke ranks with the British after forming alliance with Mir Qasim, the deposed Nawab of Bengal. He, along with Mir Qasim and Mughal Emperor Shah Alam II was decisively defeated at the Battle of Buxar on 22-23 October 1764 AD by the British and was forced to cede parts of his territory. As part of their accession design, the British appointed a resident in 1773 AD, thereby gaining control of more territory and authority in the state. The fourth Nawab was Asaf-ud-Daula (1775 AD-1797 AD) who shifted the capital from Faizabad to Lucknow in 1775 AD.
Nawab Sadat Ali Khan II and Treaty of 1801 AD: In 1798 AD, the fifth Nawab Wazir Ali Khan (1797AD–1798 AD) was accused by the British to be unfaithful and uncaring towards his own people. Subsequently he was forced to abdicate and replaced by his uncle Saadat Ali Khan II with the help from the British. The assassination of a British Resident in 1798 AD in Benares by the deposed Wazir Ali gave the British further excuse for interference in internal affairs of Awadh. Lord Wellesley exploited it to the best possible extent by virtue of treaty of 1801 AD. Saadat Ali Khan II was reduced to a mere puppet king   under the provisions of the treaty. He was forced to disband his own troops and agreed to bear the huge expense of the British army.
Annexation of Awadh with British India: The final moment came and Awadh was annexed to the English East India Company under the terms of the Doctrine of Lapse on the grounds of internal misrule on 7 February 1856 AD by the order of the Governor General of the British East India Company, Lord Dalhousie.