Yes and no.
Things are classified as secret for different reasons: National Security, Personal Security, Operational Security, and institutional protocols. In the end, keeping things secret has a finite shelf-life, and usually the larger the secret the harder it is to keep in the dark.
One - nobody outside of the commonwealth cares about Prince Phillip.
Two - it's not a matter of national security on any level.
Three - Even if it's classified due to the Royal Family's status, I doubt anyone in the UK would be shocked, nor would it cause damage to the strategic, or social status of the country.
So again you've picked to dumbest example to try to make a point about state secrets that demonstrates you don't understand state secrets, and how, and why they are kept.
It is my personal belief that people who are obsessed by the lives of the British Royal Famaily are insane.
And you don't understand how newspapers work (or used to work). Every newspaper editor dreams of breaking a story of government malfesence. After Watergate there was naked competition for the next big secret to expose, and for most of a decade all the major US, UK, French, and German news agencies did just that. Believe it or not, there was a time when government interference was met by a team of pissed lawyers, and ended with a huge payout for censorship.