The seven-year-old elephant, named Donna, was only too keen to whip her favourite treat from the royal couple's hands at the official opening of the Bedfordshire attraction's new £2 million centre for elephant care on Tuesday.
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The new facility will nurture a full herd of nine elephants with the Zoological Society of London's (ZSL) expert elephant team.
Among the friendly giants the Queen met was her namesake, Elizabeth - the youngest and most boisterous member of the group, who was born the day before the Queen's 90th birthday celebrations in 2016.
Zoological director for ZSL Professor David Field said the Queen was "absolutely delighted" to learn that the 72 stone (460kg) 10-month-old Elizabeth had been named in her honour, during a demonstration of cleaning routines in the centre's 837 square yards (700 sq km) barn.
Assistant curator of elephants Lee Sambrook, who demonstrated how keepers clean the animals' feet and inspect their teeth, said the Queen had been especially interested to hear about the round-the-clock care they receive, and compared it to keeping horses.
The Queen seemed impressed with the centre's state-of-the-art equipment and told fellow team members: "The elephants look very happy in there."
She added: "It's a rather nice change for them, I suppose."
It is 20 years since the older wing of the enclosure was last opened by Philip, who recalled the visit while speaking with Prof Field.
The Duke was "very interested" to learn about the series of technological developments the team has made since then, including obtaining a special infrasound monitoring system to pick up private elephant commutations between members of the herd.
But if Donna and baby Elizabeth seemed quite at home in the chilly spring breeze, Philip was more impressed at the hardiness of ZSL staff, declaring "You must think you're in Africa!" at the sight of Mr Sambrook's shorts.
Speaking at the unveiling of the centre's commemorative plaque, ZSL president Sir John Beddington said the facility "celebrates the exemplary care and conservation that really is at the heart of everything we do at Whipsnade".
He added: "Elephants are facing terrible threats around the world and ZSL zoos and international conservation projects are working to tackle these issues and secure a future for this amazing species."