@SuckingDieselFella How is the OP trying to frighten people by linking to the paper that informed government?
The model is not a crystal ball, it may well be flawed.
I haven't read the article in The Times (does anyone have a share token?), however, reading the quote from Neil Ferguson out of context but in context with the actual paper, I understand it to mean this:
If we follow the paper's recommendation to try and suppress the virus by the entire country socially distancing, home isolation of cases, household quarantine where there is a case, and closure of universities and schools, we can put the epidemic into reverse ie each infected person infects less than 1 other person on average (R0 < 1) so instead of the disease spreading, it starts to wane. It also means that mortality will be reduced because the best healthcare will be available. However, that will not eradicate the virus. Once you lift those restrictions, the virus is likely to start to spread again. All it takes is one single infectious person remaining in the world, or an animal. It could take decades like swine flu or it could be days.
What can eradicate the virus is herd immunity, either from a vaccine or natural herd immunity (but that would result in many unnecessary deaths). The paper is suggesting that we may need to take radical measures to control the virus until we have a vaccine. That may take many months.
The last line of the paper is referring to how people will respond to such radical and severe measures that have never happened before. As you say, that is crucial and up to us. Which is why I believe rather than scaremongering, the OP is acting responsibly in helping people understand the science and rationale behind these measures.
Kai Kupferschmidt is right that there are many caveats, some positive, some negative. Assumptions in the model about how easily the virus is transmitted, the R0 etc may be wrong but they are based on what has been observed so far. The virus may mutate, for better or worse. Drugs may become available, seasonality may help, seeing what happens in the Southern hemisphere may tell us that.
I would suggest that we all take very seriously a scientific paper and it's recommendations based on what we do know over caveats about things that we don't know, however more appealing they are. It would be wise to mentally prepare ourselves calmly for some very difficult times as the price to pay for protecting ourselves, our loved ones and saving millions of lives around the world.