In many ways, the Duchess of Cambridge is just like any other woman.

When the delicate heel of her Emmy shoes became jammed in a grate at Aldershot Barracks during Sunday’s St Patrick’s Day parade, I – and millions of other women, I am sure – winced in recognition. And when it emerged that the five-months-pregnant Duchess confided that her husband would like a girl, while she was desperate for a boy, this was merely the game played by millions of expectant parents across the country.

But – hang on a minute. Kate isn’t just any other woman. Yes, the sex of her child is out of her control – unlike her endless choice of expensive shoes and clothes. Yet given that the birth of a daughter in July would be so groundbreaking, so historic, such a breakthrough for equality, and such a role model for little girls, why on earth would she long for anything else?

While I wish Kate well, and hope she has a healthy baby, her desire for a boy is so disappointing. By transforming herself from a middle-class Middleton to the mother of the heir to the throne, she broke down the gilded barrier of royalty. Social inequality may be rife in Britain, but Kate’s marriage to William, while largely symbolic, was at least a sign of progress.

Now she is behind the barrier, she seems to be conforming to the norms of monarchy. It is unsurprising that Prince Charles has expressed doubts about the new laws of succession, currently being rushed through Parliament in time for the royal birth, which would allow a girl to inherit the throne, even if she had a younger brother. I am certain that Charles’s views are shared by other members of the Royal family. This is not an organisation that embraces change easily.

But we commoners look to Kate for progress. A girl – the descendant of coal miners as well as kings – would begin to right the wrongs visited on all those royal daughters over the centuries who should have been Queen.

It is interesting, then, that William would like a girl. Is this simply a personal preference, or something more meaningful? I’d like to think it is the latter, a remnant of his mother’s revolutionary spirit. While he was born into royalty, perhaps he is uncomfortable with the inequality in his mother’s own family, and nearly every other in the aristocracy.

Because Diana Spencer had two older sisters but, crucially, a younger brother. Sarah, Jane, Diana and Charles grew up at Althorp, the sprawling Northamptonshire family seat, but it was the youngest child who would inherit the earldom and the land by virtue of being a boy. For the girls, their way into title and inheritance was through marriage. For Charles, he simply needed to come of age.

According to the official biography of Diana, there was such consternation in the Spencer family after three girls and no male heir that her mother was sent to a Harley Street clinic so that doctors could discover what the “problem” was. This was in the 1960s. But the inequality holds fast today.

Before the new rules of royal succession, the aristocracy was already one step behind the monarchy. At least Princess Elizabeth could become Queen because she had no brother. The daughters of hereditary peers are not so fortunate, even today. If there is no son, the title goes to the next male in line – possibly a distant cousin. The girls are wrenched out of their castles. With the new succession laws, these honourable ladies will be two steps behind.

Thankfully, the royal baby has stimulated the beginnings of a quiet revolution in the wider aristocracy. Noblewomen are beginning to demand their own change in the rules. Lady Liza Campbell, whose elder sister would have inherited the Earldom of Cawdor had she been a man, is starting a campaign to demand equality, with the hope of a private member’s Bill in Parliament later this year. There are other women who agree. Julian Fellowes based the central plot of Downton Abbey, where an earl fretted over his title going to a cousin, not his three daughters, on the experience of his wife, Emma Kitchener.  She missed out on the Earldom of  Kitchener because of chromosomal chance and the title is now extinct because there was no male heir.

Why, I hear you ask, should we care about inequality in an institution that is itself so out of date? Leave the toffs to their silly rules, we have enough to worry about with our holidays in Cyprus. I would argue that, while these women may be privileged in many ways, at least most girls born into “ordinary” families are treated the same as boys. There can be few circumstances in this country where women are discriminated against at birth, but the aristocracy prides itself on this tradition, while operating in relative secrecy, without democracy. This makes change all the more necessary. Sexism is still an acceptable prejudice in the landed gentry, but very few of us take notice.

If Kate gives birth to a boy this summer, the flag-waving sections of the nation will still rejoice, but the impetus for change in the aristocracy will melt away. A historic opportunity will be missed. Kate may be wishing for a boy, but the rest of us should hope for a girl.  

Jane Merrick is political editor of ‘The Independent on Sunday’

Twitter: @janemerrick