The clip was shared ahead of the airing of an ITV documentary to mark Princess Anne’s 70th birthday on August 15.
At the start of the Zoom meeting, which took place during National Carers’ Week, the monarch’s only daughter is seen waiting for her mother to join the call from Windsor Castle.
“Good morning. I’m very glad to have been able to join you,” the Queen says as she appears on the screen sitting in an armchair in a large drawing room in Windsor.
Princess Anne asks her mother: “Can you see everybody? You should have six people on your screen.”
The Queen says she can only see four people and Anne jokes: “You don’t need me, you know what I look like.”
The full clip will be aired in an ITV documentary on Wednesday titled “Anne: The Princess Royal at 70”.
It comes as the princess paid tribute to her parents for instilling her lifelong love of nature and expressed concern over the lack of HGV drivers.
Anne guest-edited Country Life magazine this week to mark her birthday, turning her attention to how best to protect the future of the countryside.
The princess wrote about how she holds her own HGV licence, hates fly-tipping, and sees herself as she writes about rural affairs as a “classic Jack of all trades”.
“Does the little knowledge I pick up make me dangerous or well informed?” Anne remarks in the piece.
In the leader entitled “Waste not, want not”, Anne urged people to be careful about waste and energy to secure the future of the countryside.
Controlling waste is something everyone can do to help the planet, she said, adding: “Did I mention that fly-tipping is another major irritation to me?”
Discussing renewable energy, she questioned the need for wind turbines, and stressed the importance of better use of water, as well as waste from crops.
“Replacing fossil-fuel generators has not been easy, but covering the countryside in solar panels and windmills isn’t really the answer, either,” she said.
Anne added: “Small nuclear reactors could have their place, but perhaps there is not the space to pursue that now.”
The princess has held a HGV driving licence since 1974. She wrote of how her two-hour test did not cost much and featured a handling section, after which she spent the remainder of the time driving around Reading.
Expressing concern over the lack of HGV drivers, she said: “Now, it is a serious commitment in terms of time and money, which has resulted in a real shortage of HGV drivers.
“This, and the requirement for qualifications for nearly every other sort of vehicle, has made it even more difficult to maintain services.
“The needs of the rural communities during the coronavirus lockdown has underlined the importance of those people and their roles.”
- This story originally said the video call was carried out on Zoom. We have since been informed it was Cisco Webex