Nigel Farage has derided the Duke and Duchess of Sussex for their “irrelevant” social justice and environmental campaigns while abusing Prince Charles and describing the late Queen Mother as an “overweight, chain-smoking gin drinker”, in an incendiary speech to an Australian rightwing political conference.

Farage’s speech to Sydney’s Conservative Political Action Conference – from which media were barred – ranged across his views on Brexit, media bias and the United Nations, but he reserved his fiercest condemnation for members of the royal family, including princes Charles and Harry, and the Queen Mother.

The Brexit party leader was laudatory about the Queen – “an amazing, awe-inspiring woman, we’re bloody lucky to have her” – but abused her son, grandson and mother.

“When it comes to her son, when it comes to Charlie Boy and climate change, oh dear, oh dear, oh dear. Her mother, Her Royal Highness the Queen’s mother was a slightly overweight, chain-smoking gin drinker who lived to 101 years old. All I can say is Charlie Boy is now in his 70s … may the Queen live a very, very long time.”

Later, in response to a question about women choosing not to have children because of the climate crisis, he commented on Harry and Meghan’s decision to have only two children.

“Well, if I want the Queen to live a long time to stop Charlie Boy becoming king, I want Charlie Boy to live even longer and William to live forever to stop Harry becoming king,” he said.

“Terrifying! Here was Harry, here he was this young, brave, boisterous, all male, getting into trouble, turning up at stag parties inappropriately dressed, drinking too much and causing all sorts of mayhem. And then, a brave British officer who did his bit in Afghanistan. He was the most popular royal of a younger generation that we’ve seen for 100 years.

“And then he met Meghan Markle, and it’s fallen off a cliff. We’ve been told in the last week that Meghan and Harry will only have two children … and we’re all completely ignoring, the real problem the Earth faces, and that is the fact the population of the globe is exploding but no one dares talk about it, no one dares deal with it, and whether Prince Harry has two kids is irrelevant given there are now 2.6 billion Chinese and Indians on this Earth.”

Farage’s reference to “dressing up inappropriately” is an allusion to photographs of Harry at a 2005 party dressed in a Nazi uniform. Harry is now sixth in line of succession to the British throne, behind all of Prince William’s children, and will not automatically follow his brother to the throne.

The Guardian has heard a recording of part of Farage’s speech in which the Brexit party leader is laudatory about the Queen while abusing her relatives. While not on the recording, other media outlets have reported that Farage described Harry as “the prince of wokeness”. Guardian Australia has spoken to sources who said they had heard the comment, but others who said they weren’t sure or that they had not heard it.

Farage has previously canvassed his disdain for some members of the royal family.

In 2008 he was the sole MEP who refused to applaud a speech on the climate crisis by Prince Charles, later saying the prince’s advisers were “naive and foolish at best”. After Charles argued for greater legislative powers for the EU he wrote: “I seldom agree with Prince Charles … I do not think it is appropriate for the heir to a constitutional monarchy to want to take power away from his mother’s government.”

Farage was introduced to a partisan Sydney crowd of about 500 on Saturday as “quite possibly” the next British prime minister – despite not being a member of the UK parliament, and having failed seven times to be elected as an MP.

He told his Australian audience “greenies have taken over this country”, and condemned the deposed prime minister Malcolm Turnbull as a “snake”.

“Malcolm Turnbull … pretended to be a conservative but actually turned out to be a snake,” he said, comparing him to David Cameron. “David Cameron was someone who was not conservative at all, but a part of the trendy, metro, liberal elite masquerading as a conservative.”

Farage said of Turnbull’s successor, Scott Morrison, who unexpectedly won a general election in May: “You’ve now got someone conservative, mainstream media [and] those in the middle of Melbourne and Sydney may not like him … but out where real people live, they voted for him.”