Did the Britons 100 years ago have different intestinal flora and fauna?
Who said they did not have the same problems? I'm sure they did and I'm sure most of them had horrible diarrhea. 

A quick google search brought up Man and Microbes: Disease and Plagues in History and Modern Times, by Arno Karlen which states that


  In 1817, when the first cholera pandemic began [...]. In Calcutta and Jessore, cholera killed 5,000 British soldiers within weeks


However, those who survived would get used to it eventually. Cholera is much more serious than simple dysentery of course but its main symptom is also diarrhea.

The locals of wherever you happen to be are used to the pathogens that are common in the drinking water. If I am not from a place and drink water with new pathogens, I will be sick. I will also, however, eventually get over it and my body will be used to them. Depending on the details, either because I have developed an immunity or because I have developed the necessary intestinal fauna to deal with it.

So while the intestinal fauna may indeed have changed over time, this has absolutely nothing to do with what you're asking. First because your assumption is wrong (the British were subjected to the same health issues as modern Europeans visiting Asia) and second because people adapt.