William was seen leaving the private London Clinic at around 12.35pm on Thursday.
The princess, 42, was admitted on Tuesday for the successful, planned procedure but is expected to stay in hospital for 10 to 14 days before returning to her Adelaide Cottage home in Windsor.
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Kensington Palace refused to confirm what Kate was being treated for but said the condition was non-cancerous.
The King is at his private home Birkhall in Aberdeenshire, where he is preparing for the corrective procedure.
He had a series of meetings and events planned at Dumfries House in East Ayrshire today and on Friday, which are now being postponed on the advice of his doctor.
In a statement, the palace said: “In common with thousands of men each year, the King has sought treatment for an enlarged prostate.
“His Majesty’s condition is benign and he will attend hospital next week for a corrective procedure.
“The King’s public engagements will be postponed for a short period of recuperation.”
His daughter-in-law is said to be “doing well” but will spend up to three months away from royal duties.
Sky News understands the King revealed why he was going into hospital as he wanted to speak out and encourage other men to get checked. Prostate charities have praised him for his openness and candour.
It appears his decision has already had an impact with a significant increase in searches for an “enlarged prostate” on the NHS website, according to new figures.
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5:15
The Royal Family’s very eventful 2023
The NHS website’s page on prostate enlargement saw more than 11 times as many visits on Wednesday compared to Tuesday.
One in every three men aged over 50 will have symptoms of an enlarged prostate including the need to visit the toilet more frequently.
Ian Eardley, consultant urological surgeon in Leeds and national clinical director for NHS England, said: “It’s very, very common, at that age you would expect upwards of 70% to 80% of men to have an enlarged prostate.
“To some extent it is an inevitable part of ageing for just about all men.”