Well we have to take a step back to the 17th century. The rise of British banking can be accredited to the Goldsmiths. The goldsmiths began to lend the money out on behalf of the depositor, which led to the development of modern banking practices; promissory notes (which evolved into banknotes) were issued for money deposited as a loan to the goldsmith. These practices created a new kind of "money" that was actually debt, that is, goldsmiths' debt rather than silver or gold coin, a commodity that had been regulated and controlled by the monarchy. This development required the acceptance in trade of the goldsmiths' promissory notes, payable on demand. Acceptance in turn required a general belief that coin would be available; and a fractional reserve normally served this purpose.

The Goldsmith's ideologies combined together with underwriting bonds and originating foreign loans. This led to merchant banks which facilitated trade growth, profiting from England's emerging dominance in seaborne shipping. Typically as commerce and international trade grew, so did industrialization. The Industrial and banking revolution went hand and hand in a way.

The final push towards economic dominance can be accredited to the Rothschild and Baring families which established merchant banking firms in London in the late 18th century.

Tl;dr: With the economy booming, industrialization rapidly followed in order to keep up with the globalization of the economy. Fractional reserve banking, foreign loans, and growing international trades lead to technological improvements for further growth, which translated into an advanced navy.