Exports of British cotton goods to the East, mostly to India, increased by nearly 700 times by 1813. This significant increase can be attributed to several factors.

1. Industrial Revolution:
The Industrial Revolution in Britain, which began in the late 18th century, led to advancements in technology and production processes. This resulted in a significant increase in the quantity and quality of cotton goods manufactured in Britain.

2. Technological advancements:
Technological advancements, such as the invention of the spinning jenny, water frame, and power loom, revolutionized the cotton industry in Britain. These inventions enabled the production of cotton goods on a large scale, leading to increased exports.

3. Economic benefits:
Exporting cotton goods to the East, particularly India, presented lucrative economic opportunities for British traders and manufacturers. The demand for cotton goods in India was high, and British manufacturers capitalized on this demand to expand their exports.

4. Colonial control:
By the early 19th century, Britain had established colonial control over India. This allowed British traders and manufacturers to exert their influence and establish a dominant position in the Indian market. They benefited from the captive market and favorable trade policies, which further boosted their exports.

5. Competitive advantage:
British cotton goods had a competitive advantage over locally produced textiles in India. The mechanized production processes in Britain resulted in higher quality and lower-priced cotton goods compared to Indian handloom products. This made British cotton goods more attractive to Indian consumers, leading to increased exports.

6. Infrastructure development:
The British invested in infrastructure development, such as railways and ports, which facilitated the transportation of cotton goods from Britain to India. This infrastructure development ensured the efficient and timely delivery of goods, further boosting the export of British cotton goods to the East.

In conclusion, the significant increase in the exports of British cotton goods to the East, particularly to India, by nearly 700 times by 1813 can be attributed to the Industrial Revolution, technological advancements, economic benefits, colonial control, competitive advantage, and infrastructure development. These factors collectively contributed to the expansion of the British cotton industry and its dominance in the Indian market.