LONDON — The fate of a sweet-toothed TV baking contest with millions of fans has left some Britons with a sour taste.

The BBC says it has lost the rights to “The Great British Bake Off,” which it has broadcast since its first series in 2010. Rival Channel 4 offered more money to program maker Love Productions.

The publicly funded broadcaster said in a statement that “Bake Off” is “a quintessentially BBC program,” but “the BBC’s resources are not infinite.”

The BBC took the show — in which amateur bakers compete to create elaborate cakes, tortes, trifles and flans — from niche curiosity to cultural phenomenon.

Its successful recipe blends old-fashioned Britishness, a diverse array of contestants and a sprinkling of saucy humor. More than 13 million people watched last season’s finale, won by Nadiya Hussain — a headscarf-wearing Bangladeshi-British baker who has been hailed as an inspiring symbol of 21st-century Britain.

On Tuesday one of the show’s key ingredients — double entendre-loving co-hosts Mel Giedroyc and Sue Perkins — said they would quit rather than make the move. In a statement, the pair said they were “shocked and saddened” that “Bake Off” was leaving the BBC.

“The BBC nurtured the show from its infancy and helped give it its distinctive warmth and charm,” they said.

“We’ve had the most amazing time on ‘Bake Off,’ and have loved seeing it rise and rise like a pair of yeasted Latvian baps,” they added. “We’re not going with the dough.”

There was no word on whether the show’s baking judges, Paul Hollywood and Mary Berry, will make the move to Channel 4.