Her remarks emerged in clips of a conversation filmed on a phone camera during a trip to Cardiff for the opening of the Welsh Senedd.
Two video clips, parts of which are inaudible, show the Queen chatting with the Duchess of Cornwall and Elin Jones, the parliament’s presiding officer.
At one point she appears to be talking about the Cop26 climate conference, and can be heard saying she does not know who is coming to the event which will begin in Glasgow at the end of this month.
In the clip, she said: “I’ve been hearing all about Cop…I still don’t know who’s coming.”
In a separate clip, the Queen appears to say it is “irritating” when “they talk, but they don’t do”.
Ms Jones then appears to reference the Duke of Cambridge in her replying, saying she had been watching him “on television this morning saying there’s no point going into space, we need to save the earth”.
The Earl of Strathearn had earlier warned the COP26 summit against “clever speak, clever words but not enough action”.
He said: “I think for Cop to communicate very clearly and very honestly what the problems are and what the solutions are going to be, is critical.
“We can’t have more clever speak, clever words but not enough action.”
Prince William has criticised the space race, saying the world’s greatest minds need to focus on trying to fix their own planet instead, the day after Star Trek’s William Shatner made history by becoming the oldest person in space in a rocket built by Amazon founder Jeff Bezos’s space travel company Blue Origin..
Transport Secretary Grant Shapps said comments made by the Queen should “stay in private”.
“I think comments made in private should stay private, but we all share the desire to see progress made and we know there will be hundreds of leaders coming to Glasgow for Cop,” he told Sky News.
“We will wait to see whether it lives up to – whether they all live up to – expectation, it’s very important we get this job done.
“I don’t think her comments were for broadcast.”