Of the traced outbreaks, most were in schools. But that is not really a surprise, as outbreaks in schools are really easy to trace. If you have a group of 25 students which basically spend 40 hours a week together and they all get sick, super obvious. But how do you trace clients of a restaurant back to a restaurant? You mostly don't.
My reading of these lists is as a mix between places that are easy to trace, and places where really a lot of infections are happening. It is hard to tell which are which and which are both. Not to mention where the other missing 80% of cases came from.
Weirdly I see slightly different numbers... Table 2 on page number 26 of the first pdf? Sorry if I'm looking in the wrong place...
Either way, I think this relies on contact tracing data, but contact tracing doesn't happen on trains or in supermarkets (super markets are exempt why exactly? No one knows). That's why their zeros...
Schools, hospitals, care homes, and workplaces account for the huge majority of spread. There's no empirical reason to think either tube trains or supermarkets are the problem.
[1] https://www.gov.uk/government/statistics/national-flu-and-co...