This is quite a late one but there's a reason for the late reply.
Sky news has been using this chart from time to time the last 24 hours. Myself personally I'm not particularly a visual communicator I know that Italy has implemented three lock downs and another three substantial restrictions and when they happened. If it helps others then why not.
On a technical point there are a couple of reasons why the government may not particularly like using it. The DCMO got drawn a little bit too much, in an answer to a question, to talking about the case rates, the death rates in Italy and here someone partially quoted what they said. I'm not quite sure why the PHE/government view focuses on this a bit too much. It may be that the government side is worried about criticism (although there's a flippant answer to that and that if they are worried about how the death rates appears to the media, if we get our testing regime frigging sorted it'll look better). Another technical point the DCMO alluded to that hasn't been picked up, it is generally reckoned that in bits of Italy particularly 5 or 6 provinces people are dying at home and so not part of the hospital numbers and not part of the death count (in the UK this isn't happening). Sadly, this is very plausible. One of the interesting bits in different bits of Italy is people have said they hear 'fewer ambulances in these days'. That could mean the virus is under control, or it could just mean that they aren't taking people to hospital.
In terms of communicating to the public, I feel that Boris does a particularly poor job on this one. The best team to communicate it at press conferences is probably DCMO Jenny Harries. You could also draft in Queenie at some point.
In terms of what's in the content as on this forum a lot of people in government are in highly professional jobs, are in the position of being privileged, very powerful, having their opinions listened to and so go off on one and think the public are morons. This tends to lead to being quite vague as is seen in some press conferences - not knocking having an epidemic curve in an early press conference it was good, but it was the verbal said that was good and not the graphics! The public understand what an exponential curve is, contrary to what particularly 5 or 6 people on this forum think. The alternative theory is that people think keep it simple (which has also been discussed on this thread). Content needs to focus on the specifics of social distancing. As said just yelling social distancing to everything doesn't work. It's one that many countries have grappled with as they've imposed numeric bans on groups of 50 or in Germany yesterday more than 2. A 5 minute video that is repeated throughout the day with medics, queenie, DCMO, videos and graphics and clearer advice is what's needed. Press conferences although useful just appeal to the vanity of politicians and journalists.
Lastly the person who goes most 'off message' from a politician's point of view, but not a scientific or reasonable one is DCMO Jenny Harries. The mental health side is clearly important to the medics and scientists. This isn't coming across to a society or media that's only really starting to talk about it. It's because it's something at societal level we're very bad at.