Housing in London is predominantly row-houses, with mostly one toilet which may be adequate for family of 2. However, the housing values have gone thru the roof in last 2 decades, making them unaffordable and forcing many grown kids to live with their parents. So family of 4 or 6 is not uncommon sharing only one toilet in the morning toilet rush hours.
A single toilet is common in the U.S as well, I have never heard of it being used as an excuse for Americans to defecate in public.
You should rethink that excuse, row houses in London sound pretty normal.