Maybe you've seen this article
History of Cholera? The dates fit with what you noted.
Essentially it is saying that the disease has been around for thousands of years with recorded descriptions of epidemics in India and maybe Greece. In 1817 a worldwide pandemic spread from India.
In 1854
the famous Broad St epidemic occurred in London. It is a fascinating story. Dr John Snow collected meticulous data demonstrating the initial source was a family that got rid of their sewage in their basement. That leaked into the water supply which was obtained by the local population via the Broad St pump.
Before that time the disease was believed by the other doctors to be from 'miasma' meaning bad air. It made sense to them given how bad the smell was in the area near the river and it was that area the infections were concentrated.
This was the beginning of epidemiology and the first time it was recognized that microorganisms were the cause of infections.
The doctors dismissed Snow's findings for another ten years. When you read how detailed of a case Snow made you have to wonder what was wrong with them. What was wrong is the human tendency to believe what they already know and resist anything that contradicts those beliefs. They were sure miasma was the cause of cholera in London.
Snow was able to convince the city authorities and they removed the handle of the Broad St pump. The epidemic subsided.
Thus the Broad St pump handle became famous. I love it.
One point for your story is that the recognition of microorganisms causing infections wasn't known until the 1850s. Your characters might know the water is making people ill but they would have no idea that bacteria was the cause. And it is unlikely they would know much about cholera since as you note, it didn't reach London until the 1830s.
They wouldn't know what was causing people to get ill. They might, however, recognize bad water was a cause of disease. Contaminated water could have simply been the cause of disease with any number of organisms. Diarrhea from contaminated water is still one of the leading causes of childhood deaths in much of the third world. There is no single pathogen causing those deaths.
How does the specific disease fit in the story given
no one knew about infectious disease being caused by microorganisms at the time?
If you need an outbreak with an abrupt beginning you don't need to name the pathogen, any number of things could cause an outbreak.