The Thames
In order to clear the city of miasma, London was faced with the issue of clearing out the waste. Ultimately, Johnson tells us that this would lead to the Thames becoming a "river of sewage," but would still ironically be better than the alternative.
Dramatic irony
As readers, we have the benefit of hindsight when reading about the cholera epidemic in London. We know what happened and that eventually the epidemic was halted; as such, there is a sense of dramatic irony.
London
Although London is nowadays seen as a prospering city, Johnson tells us what London ironically used to be like hundreds of years ago. He comments on the dirty streets, unhygienic living conditions, and the fact it was overpopulated.
The cause of the outbreak
The cholera outbreak in the 1800s was ironically caused by a single woman who threw away her son's diapers. We might expect an epidemic to be caused by something more dramatic, or to not have a single identifiable cause.
Miasma theory
As readers, we learn about the theory of miasma and the theory of contagion. With the benefit of hindsight and scientific discoveries, we know how diseases really spread.