Many thanks - that is most helpful. I had originally assumed that the idea that "Wellington introduced wellington boots into the army" was a red herring, but had begun to have doubts. I don't actually need to say that it is definitely wrong - I simply won't mention the point.
The original wellingtons were a tremendous success: Wellington got Hoby to make the first pair in 1817, and I've seen an 1821 advertisement in a Dublin newspaper which refers to 'wellington boots' in a list of other styles with no need of an explanation. I understand that they remained very popular until about the 1850s when tastes changed to a shorter boot. Remember that even in the city, the streets were pretty dirty, and England doesn't have the driest climate.