The comedy returns to screens on Saturday for the first time in 24 years when it airs on the Britbox streaming service.
The first installment of the 10-part series sees the makers of the programme mock celebrities, the royal family and politicians of all stripes.
The episode opens with a joke at the expense of the Duke of York, who finds himself being struck in the face after following the advice of television producers in an apparent reference to his interview with the BBC’s Newsnight.
Government adviser Mr Cummings, who is depicted as an evil alien overlord, repeatedly comes into the satirists’ firing line during the episode.
He refers to Prime Minister Boris Johnson’s baby as looking “delicious” and asks if he can eat him.
Mr Cummings also asks Mr Johnson a number of times if he plans to fire him, to which he is repeatedly told no.
Harry and the Duchess of Sussex are also depicted in pursuit of a normal life in the US in the series.
Harry is shown job-hunting as he looks for a regular career, but finds he is ill-equipped for the modern workplace.
Environmental activist Greta is also depicted as a weather woman who tells viewers in a panicky voice that the weather is going to be “hot”.
The episode included references to recent news stories including Mr Trump contracting coronavirus and the US presidential debate.
Speaking at a screening of the episode, Spitting Image co-creator Roger Law said: “The new Spitting Image is going to be a circuit-breaking, satirical moonshot with a unique ability to satirise the good and the great.
“We will take back control from losers like Boris and Trump and have fun with Kim Kardashian and Kanye West and there will be tongue lashings from our weather girl Greta Thunberg.
“You will be amazed by Beyonce and Jurgen Klopp and incredibly irritated by James Corden and knocked out by Tyson Fury.
“This time Spitting Image is going global.
“Aussie Tony Abbott has signed up world-beating deals with Albania, North Korea and Outer Mongolia.”
He added: “Everything we have created for the shows, the puppets, the satire, has been done in the public interest.”
Spitting Image originally ran for 18 series between 1984 and 1996 and was watched by 15 million viewers in its heyday.
A new episode of the comedy will be available on Britbox every Saturday for 10 weeks.
