They were silencing whistleblowers when they knew there was an outbreak of a dangerous respiratory disease and misleading the public about the communicability of the virus causing it. The city authorities in Wuhan allowed a large feast attended by an estimated 40,000 families to take place on the 18th of January. A study estimates that they could have reduced the number of infections in China by 66%, 86%, or 95% if they had acted one week, two weeks, or three weeks sooner, and this would likely also have reduced the number of outbreaks seeded around the world by travellers from Hubei province.
Effect of non-pharmaceutical interventions to contain COVID-19 in China | Nature
New Zealand blocked entry to the country for travellers originating from China, or who had been in the country in the past fourteen days, on the 3rd of February. It did not announce a quarantine for all travellers into the country until the 16th of March, and did not go into full lockdown until the 26th of March.
Those figures on China acting early are in relation to preventing local infection levels - in the area where they apply the lockdown. Those figures do not apply to the global spread rates for two very obvious reasons: the virus emerged in November, and it has left the country before being known as a threat.
It was not until the 27th December that the authorities were notified meaning for up to 2 months the virus had been spreading and almost definitely had left Wuhan. Again, the time line you're proposing hinges on an impossible level of foresight.
Chinese scientists had not even confirmed human-to-human transmission until the 20th Jan, and it's irrational to bolt people into buildings based on suspicion.
As we've seen from the people in our own country, a large amount people will ignore lockdown orders the second it interferes with their plans. Now imagine those people are not even aware of the new virus.
On the 20th human to human transmission was confirmed.
Three days later, the measures they developed after SARS was activated, putting Wuhan in lockdown. That's a turnaround time of 26 days from first discovering the virus to:
1) Closing the origin site
2) Publicly releasing the genome and that its of the SARS family.
3) Shutting people in.
It was in the 14th, 17 days into the timeline that front line hospitals suspected human-to-human transmission due to the number of cases. It had not yet been objectively confirmed. It had also entered Thailand and the US by then.
It's also likely China was suffering from a severity bias. When it first became aware of the disease, it was due to 27 cases of pnemuemonia, 7 of which being critical cases. That indicated a severity in line with MERS (R0 0.5) and Sars (R0 0.2-1), which are damaging enough that large scale spread of it is difficult. It wasn't until later it was discovered that all of the more minor cases were also the same disease.
China does horrible things. But blaming the shit handling of the Virus by the UK and US governments on them is daft. By the time the first case arrived here preventing travel from China was already too late; and we don't even know for sure when the first case arrives, only the first severe case as the UK figures for cases also suffer from a severity bias for a long time.