Kate, 42, revealed she was undergoing preventative chemotherapy in an emotional video message on Friday.
The announcement came after weeks of intense speculation and conspiracy theories on social media.
Paddy Harverson, who was previously the official spokesman of Kate and the Prince of Wales, was asked on the BBC’s Sunday With Laura Kuenssberg programme where the responsibility for the pressure lay: social media or mainstream media.
“Well, it feeds off itself,” he said.
“It’s a sort of permanent doom loop. And it’s the worst I’ve ever seen.”
However, he said the royal family still would have done the announcement in the same way, even without the pressure.
“I’m absolutely convinced that if we hadn’t had all the madness and social media, if we hadn’t had the Mother’s Day photo mistake, they would have still done it like this,” he said of Kate’s video statement on Friday.
“They would have still waited till this last Friday when the schools are breaking up to make the announcement.”
Mr Harverson denied the institution was “fragile” now the King and the Princess of Wales are receiving cancer treatment.
“We just have to come to terms with the new reality, there’s fewer of them,” he said.
“So, everyone just needs to sort of understand that they will still be busy, they will get over this. I am highly confident that the King, who I know well, is incredibly strong, very resilient, a great spiritual person, so I know he’ll get through it.
“Likewise with the princess, with Kate, I think once they’re through this sticky patch, I think we’ll get back to normal.
“I think the nation just needs to adjust, and the media, and everyone who follows this, to a smaller family but still very busy doing what they do in their own way.”
There has been a global outpouring of support, including from the King, the Duke and Duchess of Sussex, political figures and members of the public.
On Sunday, Chancellor Jeremy Hunt praised the “incredible stoicism” of Kate and the King.
He also told Laura Kuenssberg: “My thoughts are also with the Princess of Wales and the King, and how much I think we all admire their incredible stoicism.”
Labour Party chairwoman Anneliese Dodds said she felt a “huge amount of sympathy” for Kate while watching her announce her cancer diagnosis on Friday evening.
Rumours online about the princess intensified after William missed, at very short notice, the memorial service of his godfather the late King Constantine of Greece on February 27.
It is now understood the prince’s decision not to attend was related to his wife’s condition, but it is not known when the princess was told about the positive test for cancer.
Further speculation was triggered after the princess admitted to “editing” her official Mother’s Day photograph which had irregularities.
A further development saw an investigation launched by the UK’s privacy watchdog, the Information Commissioner’s Office, into allegations there were attempts to access Kate’s private medical records at the London Clinic where she had her surgery.
It is not known how long Kate will be receiving treatment but it is understood she may be keen to attend events as and when she feels able to, in line with medical advice, although this will not indicate a return to full-time duties.
William will continue to balance supporting his wife and family, and maintaining his official duties as he has done since her operation.
The prince is due to return to public duties after his children return to school following the Easter break.
He and his wife will not attend the royal family’s traditional Easter Sunday service at Windsor Castle’s St George’s Chapel, which the King is hoping to go to with the Queen if his health allows.
It is not likely to be a large family gathering or service, according to The Telegraph, as Charles has paused public-facing royal duties.
Charles has been receiving treatment for an undisclosed form of cancer since early February after he was treated for an enlarged prostate at the same hospital where Kate had abdominal surgery.