Theresa May has described the decision to drop the word Easter from the name of Cadbury and National Trust egg hunts as "absolutely ridiculous".
Her comments come after the Archbishop of York said calling the event the Cadbury Egg Hunt was like "spitting on the grave" of the firm's Christian founder, John Cadbury.
But Cadbury said Easter was referred to on much of its packaging and marketing.
The National Trust also denied it was downplaying the significance of Easter.
It said there were more than 13,000 references to Easter on its website and that it runs a programme of activities to mark the event.
Meanwhile, a descendant of John Cadbury pointed out that "as a Quaker, he didn't celebrate Easter".
His great-great-great-great-granddaughter, Esther McConnell, said: "He believed that every day is equally sacred and, back then, this was expressed by not marking festivals."
She added: "I am glad to see that Cadbury and the National Trust are welcoming those of 'all faiths and none' to their event regardless of whether they call it Easter or not."
However another distant relative, his great-great-great-grandson James Cadbury, said the National Trust "should have made sure that the word Easter was used".
Quakers are members of a faith group with Christian roots, but they do not celebrate Christian festivals such Easter and Christmas.
The British Humanist Association (BHA) described the issue as a "storm in an eggcup".
'Very important festival'
The annual egg hunts at National Trust properties around the country over the Easter weekend have been run in partnership with Cadbury for 10 years. About 300 will be taking place this year.
The event has previously been called an "Easter Egg Trail" but this year it has been promoted as "Cadbury's Great British Egg Hunt". Both organisations do refer to Easter within their promotional adverts.
Mrs May told ITV News: "I'm not just a vicar's daughter - I'm a member of the National Trust as well.
"I think the stance they have taken is absolutely ridiculous. I don't know what they are thinking about frankly. Easter's very important... It's a very important festival for the Christian faith for millions across the world."
Archbishop of York John Sentamu said Mr Cadbury, a Quaker who founded the firm in 1824, was renowned for his religious beliefs and would not condone dropping the word Easter.
He said if people were to visit Cadbury World in Birmingham "they will discover how Cadbury's Christian faith influenced his industrial output".
"To drop Easter from Cadbury's Easter Egg Hunt in my book is tantamount to spitting on the grave of Cadbury," Dr Sentamu added.
A spokesman from the Church added: "This marketing campaign not only does a disservice to the Cadburys but also highlights the folly in airbrushing faith from Easter."
Labour leader Jeremy Corbyn said the issue reflected "commercialisation gone a bit too far".
The National Trust said the suggestion it was downplaying the significance of Easter "could [not] be further from the truth".
"A casual glance at our website will see dozens of references to Easter throughout," a spokesman said.
But some National Trust members contacted the BBC to say they were considering cancelling their memberships over the row.
The trust updated its website on Tuesday morning to add the word Easter to a page promoting the event.
In a statement, Cadbury said it had used the phrase Easter in its marketing for over 100 years and "continues to do so in our current campaigns", adding: "We invite people from all faiths and none to enjoy our seasonal treats."
Richy Thompson, BHA's director of public affairs, said: "Easter is a fun time of year for people of all ages and beliefs. It's disappointing that the Church saw fit to whip up a storm in an eggcup over this and in a bid to maintain its relevance in an increasingly non-religious country."
Paul Parker, recording clerk for Quakers in Britain, explained why Easter - and other traditional festivals - are not celebrated by Quakers.
"Eggs - chocolate or otherwise - remind us of new life and new beginnings. Quaker faith prompts us to seek that of God in each other," he said.
"Rather than keeping traditional church festivals, Quakers say every day is a chance for new beginnings for all of us, for love and forgiveness, restorative justice and joy."