The people we are seeing dying now have probably had this for about 3-4 weeks, based on what seems like the usual progression of cases. At the start of March, social distancing still wasn't really a thing, we were still very much debating what to do about this- most people were behaving as normal. Many people had just recently come back from ski holidays in Italy and were carrying on as normal if they had no symptoms. At the start of March, people were still debating going on holiday.
16-19th March was the Cheltenham festival (60,000 people from all over the world attending daily), 11th March was Liverpool vs Athletico Madrid. From last week into this week, I think some people who attended those events will start to show symptoms, but we won't see this reflected in the figures until they start getting ill enough to go to hospital (probably next week).
I think it'll be interesting to keep an eye on Ireland's figures over the coming week- a lot of people fly over from Ireland for Cheltenham. At the moment, their figures are quite low, so any spike will be noticeable.
I hope I'm wrong about all of this, though!