Final answer:
Soane designed the London headquarters of the Bank of England, an important institution responsible for issuing banknotes and managing monetary policy.
Step-by-step explanation:
The London headquarters of the important institution designed by Soane is the Bank of England. The Bank of England, also known as the Old Lady of Threadneedle Street, is the central bank of the United Kingdom. It was founded in 1694 and is responsible for issuing banknotes, managing monetary policy, and promoting financial stability in the country.
Soane's design for the Bank of England was completed in 1797. He created a neoclassical building with a pedimented facade, columns, and a grand banking hall. His design showcased his innovative use of light and space, with large windows and skylights to illuminate the interior.
The Bank of England's London headquarters plays a crucial role in the country's economy and financial system, and its architectural significance makes it an important landmark in the city.