The last outbreak appeared to have been in 1866 but there were further smaller outbreaks in the 1870s.
The last great outbreak of
smallpox (Variola Major) in the British Isles was 1871-72 which caused approx. 42,000 deaths in England and Wales. The last epidemic of smallpox to afflict the British Isles was 1901-02,this was the last severe occurrence of smallpox on a widespread scale in Britain's history, claiming 1,300 lives in London and 1,400 in Glasgow.
There were no epidemics of Typhoid , but there were Cholera epidemics in 1832, 1848-49, 1853-54, and 1865-66.
Smallpox is transmitted from person to person primarily via contaminated particles from the nose or mouth. Cholera is a water born disease. Typhoid (caused by a bacterium) is most common in tropical climates usually caused by contaminated water or food. There was a typhoid epidemic in the Boer War which killed 13,000 troops.
Details from the "Encyclopedia of Plague and Pestilence"
Whooping cough, measles, scarlet fever, diphtheria, smallpox, typhus, typhoid, and tuberculosis were endemic during the 19th century. So there need not have been an epidemic as such.
Stan