To William and Kate, a daughter - but will she be queen one day?

In her coronation pledge, the queen promised to “maintain in the United Kingdom the Protestant Reformed Religion established by law” and to “maintain and preserve inviolably the settlement of the Church of England”.

Like her predecessors, a day later the queen swore the Scottish oath before the Accession Privy Council, where she pledged to uphold the Church of Scotland and the Presbyterian form of Church government in Scotland.

The law barring marriage to a Catholic dates back to the 1701 Act of Settlement when Protestant England fretted that the death of William of Orange could see a return of the Catholic Stuarts.

In a report last year, MPs noted that the decision to abolish the ban barring monarchs-to-be from marrying Catholics could have “one possible consequence”.

“The proposal thus raises the prospect of the children of a monarch being brought up in a faith which would not allow them to be in communion with the Church of England,” said the Commons Political and Constitutional Committee.

The rule under Catholic canon law can be put to one side through papal dispensation and, indeed, that has already been done in the past for the Windsors in the case of Prince Michael of Kent.

However, Dr Bob Morris of University College London has pointed out that much may have changed long before Prince William gets to the throne, let alone any of his offspring.

“It is well known that Prince Charles is interested in other faiths and wants to be regarded as ‘Defender of Faith’ rather than ‘the Faith’,” he told a Commons inquiry last year.

However, the monarchy is nothing if not flexible, even if its ability to change is hidden behind a panoply of tradition and pomp – as was shown in the days before the queen herself took the throne.

King George VI’s death in 1952, according to Prof Robert Blackburn, created a situation where for the first time in British history a monarch died leaving two daughters, but no sons.

Under the old, feudal law, the then Princess Elizabeth should not have ruled alone, since the crown should have been shared with her sister Margaret as “that is how mediaeval property law worked”.

Such a course, however, was deemed to be nonsense, leaving the Privy Council to declare the common-sense solution to be that the eldest daughter should reign alone. The last 60 years could well have turned out very differently.