The period, 1750-1900, roughly corresponds with the Industrial Revolution, a time of rapid economic growth in Britain. As the country's capital, London was hugely affected by these changes, in a number of important ways.
Firstly, by far the most striking change in this period was the population. At the beginning of this period, for example, London had a population of 750,000 people. But this increased substantially over the course of the next century: from 3.1 million people in 1860 to over 6 million by 1900. There are a number of reasons for this population boom, including rising rates of immigration and the rise of urbanisation, as people flocked from the countryside to find jobs in the industrialising cities. You can find out more in the first reference link provided.
Secondly, London transportation underwent significant changes in this period. In the 1700s, for instance, London's roads were in a sorry state of disrepair. They were prone to flooding and journeys out of the capital took a long time. It took over two weeks to get from London to Edinburgh, for instance. But all this changed with the coming of the Industrial Revolution. A great boom in road-building began in the 1780s which made travel far easier than before. By the 1830s, for example, the above journey to Edinburgh took only two days. The number of stagecoaches (covered wagons) increased too, to ferry people and resources across the capital and beyond. Improved coach architecture continued to improve these coaches, making them bigger, more efficient and able to carry heavier loads. London's first railway opened in 1838, prompting a new era in transportation and connecting London to the rest of the country. The famous London Underground also opened in 1863. Please see the second and third reference links for more information.