The Queen shows Sir David Attenborough around the Palace garden for ITV show

Viewers will see the sovereign laughing and trading dry observations on modern life with the television naturalist and fellow 91-year-old.

At one point, the pair discuss the creation of a canopy of trees across the Commonwealth to mark her reign.

But the Queen discovers that there can be drawbacks to a growing layer of foliage in her own backyard.

When he teases her about a 50-year-old sundial that is shaded by trees, she orders it to be moved into the sun after escorting Sir David around the Buckingham Palace garden.

“A sundial – neatly planted in the shade,” the veteran broadcaster observes in that voice so familiar to fans of natural history programmes.

“Isn’t it good, yes,” the Queen replies with a trace of sarcasm, asking her head gardener: “Had we thought of that? It wasn’t in the shade originally, I’m sure. But, erm...maybe we could move it.”

Sir David responds: “Well it depends whether you want to know the time or not.” Her gardening staff confirmed that, after the conversation, the sundial was indeed moved away from a clump of the 1,400 trees in the palace garden.

The scene is one of a number of exchanges between the pair – born a few weeks apart – that were recorded for ITV documentary the Queen’s Green Planet, to be aired next Monday.

They were filmed during an unscripted 90-minute tour of the 40-acre garden as part of the programme about the Queen’s Commonwealth Canopy.

This is an ambitious project to persuade the 53 Commonwealth nations to each create an area of protected forest to mark the monarch’s extraordinary reign and her legacy as head of the organisation of mainly former British Empire countries.

Filmmaker Jane Treays said of the programme: “I was aware I was working with the two most consummate professionals on the planet.”

She admitted the experience exceeded even her expectations, adding: “It was probably the most magical afternoon of my career.”

At one stage, they are interrupted by the sound of a helicopter. “Sounds like President Trump, or President Obama”, the Queen says.

She gets her own back on Sir David by teasing him when he gets muddled about the location of trees planted by the Queen to mark the births of each of her children. He mixes up the name tags for Andrew and Edward, identifying both as Andrew when he bends down to look. “You said that was Andrew. Can’t both be,” she says.

Sir David has since cheerfully admitted: “I couldn’t find my glasses.”

Like many a pensioner, the pair are recorded complaining about health and safety and attempts to prevent children playing conkers.

During another humorous moment the head of state spots a young sapling bent over and quips: “That one we won’t look at because it doesn’t seem to be doing very well."

“Are you sure that’s meant to be like that?” she says to someone off camera, adding “Somebody sat on it I think, at the garden party.”

The Queen’s Commonwealth Canopy was the idea of Labour MP Frank Field, who found successive governments lukewarm about it until the monarch supported the project.

So far 40 Commonwealth countries have created a Queen’s Canopy, with 13 still to act.

Mr Field has called for the Queen to be given the Nobel Peace Prize for keeping the Commonwealth together during her 66 years on the throne.

The Queen’s Green Planet is on ITV at 9pm on Monday April 16.