It’s still morning in London but they’re already gulping the Champagne outside St. Mary’s Hospital where Duchess Kate of Cambridge has given birth to her second royal baby, a new princess for Britain.

Millions of Brits were hoping for — and betting on — a girl to join Prince George in the Cambridge family. She is Queen Elizabeth II’s fifth great-grandchild.

But feminists everywhere might want to sip some bubbly, too, because this baby girl marks a major shift in the ancient (nearly a 1,000 years old) and resolutely patriarchal institution of the world’s most famous monarchy.

For the first time, under recently changed rules approved by Britain and the 15 other Commonwealth countries that retain the monarchy, birth order will trump gender in the succession line to the throne.

The new princess (her name has not been announced yet) will be fourth-in-line, and will remain so even if she later has a younger brother.

As a practical matter, the new “spare to the heir” probably won’t ever actually reach the throne; older brother Prince George is more likely to be a future king.

But spares have inherited in the past and this princess won’t have to take a place behind her younger brothers, the way numerous female ancestors did.

The most recent: Princess Anne, the queen’s only daughter and her second child, has two younger brothers who take precedence over her in the succession. And all of Anne’s descendants are lower on the ladder, as well.

It has ever been thus in Britain, and before that England and throughout most of Europe. Female monarchs were an anathema for hundreds of years; princesses always took a back seat to sibling princes, and were mostly married off for political and strategic alliances with little to say in the matter.

Even when a princess had no brothers, she could be denied the crown, which would then pass to another male relative (think the original inheritance problem in Downton Abbey).

This happened to one royal woman in the 12th century; she sought to claim the English throne as her father’s only surviving child but civil war erupted and her male cousin ended up with the prize.

The preference for males in the monarchy was so strong that England didn’t get its first undisputed female sovereign until 1554 when Henry VIII’s elder daughter, Queen Mary I (aka Bloody Mary), succeeded her sickly teen-age half-brother.

There have been only five reigning queens since, but at least three of them, including the current queen, Queen Victoria and Queen Elizabeth I, are considered among the best of the 40 monarchs since 1066.

So the changes in the British succession rules, which were approved with almost no opposition, are historic, just as this new little princess is historic.