Rishi Sunak sent a message to Prince William and Princess Kate after an alleged breach of the Princess of Wales's medical data.
Downing Street has urged the British public to "get behind" the Princess of Wales as she recovers from surgery.
This is amid multiple conspiracy theories about her health and an alleged data breach at the hospital where she was treated in January.
The Prime Minister's official spokesperson issued a statement after claims emerged that staff at the private London Clinic where Kate underwent an abdominal operation illegally tried to access her medical records.
Kate has been the victim of an alleged security breach
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Asked about the alleged breach at the London Clinic, the spokesman said: "Clearly there are strict rules on patient data that must be followed."
And on whether people should leave Kate alone, they added: "I think we all want to get behind the Princess of Wales, and indeed the Prince of Wales, and we obviously wish her the speediest of recoveries."
Three staff members at the London Clinic are being investigated after allegedly trying to view the princess's records without authorisation.
The clinic itself says it will take "all appropriate steps" to investigate the alleged breach.
Rishi Sunak has issued a message for Princess Kate
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Its chief executive, Al Russell, said: "Everyone at the London Clinic is acutely aware of our individual, professional, ethical and legal duties with regard to patient confidentiality.
"We take enormous pride in the outstanding care and discretion we aim to deliver for all our patients that put their trust in us every day.
"We have systems in place to monitor management of patient information and, in the case of any breach, all appropriate investigatory, regulatory and disciplinary steps will be taken.
"There is no place at our hospital for those who intentionally breach the trust of any of our patients or colleagues."
Kate has been the victim of an alleged security breachGettyThe princess is said to be aware of the allegations, while a spokesperson for Kensington Palace said: "This is a matter for the London Clinic."
The Information Commissioner's Office has said: "We can confirm that we have received a breach report and are assessing the information provided."
Ingrid Seward, royal biographer told the Mirror the news will have come as "a shock to the Palace, a shock to the princess and a shock to her husband and (to her) father-in-law, the King".
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Kate underwent an abdominal operation at The London Clinic in JanuaryGettyShe added: "For the London Clinic, it is an embarrassment of the worst kind and they will do their best to appease everyone concerned.
"As for Catherine it is another emotional upset; she is going to have to put behind her.
"She is far stronger than she looks. She will not allow her battered emotions to get the better of her."