Every well-run firm has to engage in succession planning, but not everyone has to plan for The Succession, as Britain’s royal family is patiently doing.

On Wednesday, Prince Charles, along with his wife, the Duchess of Cornwall, accompanied Queen Elizabeth to the houses of parliament for the queen’s speech. Much was made of the fact that it was Charles’s first time to do so for 17 years; even more that the duchess wore a tiara that once belonged to the Queen Mother, loaned for the day by the queen.

The image of the queen travelling in the Irish State Coach with Charles and Camilla from Buckingham Palace prompted febrile chatter of abdication, or the creation of a regency.

For now, such speculation is merely that – even if Wednesday’s events came after news that Charles will take his mother’s place at November’s Sri Lanka Commonwealth summit.

Pressed with questions about her intentions, Buckingham Palace denied that there had been discussion about a regency, saying that the queen’s robust health continues.

Now 87, she still carries out 400 engagements and went riding in Windsor last Friday, courtiers “let it be known” this week, as these things are done in the world of royalty.

Regencies, in any event, have only ever been established when a monarch has been too ill to reign – although Britain’s last experience in the early 19th century was not a happy one. Then, George III was deemed unfit, leaving his son, George, the Prince of Wales, to take over, where he continued the dissolute life that he had led as understudy.

If a regency is unacceptable to the queen, an abdication – following the example of Queen Beatrix of the Netherlands last month – is unthinkable.

Firstly, she believes strongly that she swore to a lifetime of duty, while, just as importantly, talk of abdication evokes unwelcome childhood memories of the abdication of her uncle Edward VIII in 1936. Then just 10, the chapter was “exceptionally unsettling” for her, says constitutional expert Prof Noel Cox of the University of Aberystwyth.

“When I broke the news to Margaret and Lilibet that they were going to live in Buckingham Palace, they looked at me in horror,” recounted their nanny Marion Crawford. “ ‘What?’ Lilibet said. ‘You mean forever?’ ”

Nevertheless, there is a changing of the guard taking place, slowly but perceptibly. The younger royals, William, Kate and Harry, were sent on foreign duty last year for the diamond jubilee.

So far, the strategy has been a glorious success, from the point of view of the royal family – “‘The Firm”, as Queen Elizabeth’s father, George VI, described it. Indeed, 2013 should mark another good year for royalty, topped by the birth of a child in July to Prince William and the Duchess of Cambridge.

Significant sections of the British public remain lukewarm about Prince Charles’s accession to the throne, although perhaps less so than they once were. Meanwhile, talk of change has come in a week when the Guardian has gone back to court to challenge the British government’s refusal to disclose Charles’s letters to ministers.

Dubbed “the black spider memos” because of his hand- writing, they are known to be frank, opinionated and often seen as interfering by some of those who have received them over the years. Refusing to release them under the Freedom of Information, attorney general Dominic Grieve has said publication would “damage the Prince of Wales’s preparation for kingship”.

Once on the throne, Charles will pass the title of Prince Wales on to his eldest son, William. He is expected not to reign as King Charles but rather George VII, given the unhappy ends for Charles 1 and II.

Most importantly from William’s point of view, he and his wife will become the Duke of Duchess of Cornwall and Cambridge, not just of Cambridge.

While the title of Prince of Wales brings rank, the Duchy of Cornwall brings the wealth that has funded the household of the heir-in-waiting for centuries. The duchy is in good health, with its income rising in 2010 – the last year for official figures – to £17 million, which led to Charles receiving a tax bill of £4.5 million.

In an archaic quirk, Prince Charles is entitled to the assets of those who die in Cornwall without leaving a will – which saw him receive £450,000 in the last year alone.

However, even royalty is not completely immune to economic woes, judging by the prince’s decision this week to close a vegetable shop in Tetbury in Gloucestershire, which has sold produce from his Highgrove estate for the last eight years.

Besides the patronage of the prince, the store became well- known for selling perfectly edible if oddly shaped organic produce – the kind that would not pass muster with inspectors from the supermarkets. Three jobs will go, but Highgrove is hopeful that two can be created by expanding home deliveries of vegetables and meat – although that service has been suspended because the absence of spring has meant that there are no vegetables to sell.