The Princess Royal “is fine”, her husband has said, after she sustained minor head injuries and a concussion thought to have been caused by a horse.

Vice Admiral Sir Tim Laurence left the hospital where she is being treated after a nearly two-hour lunchtime visit.

As he left the main entrance of Southmead Hospital, Bristol, at about 2pm, he said: “She’s doing fine, slow but sure.”

It is the first update on Anne’s condition since Monday, when Buckingham Palace said she had suffered minor injuries to her head and concussion.

Asked if he had taken anything for the princess, Sir Tim said: “Just a few little treats from home.”

He was wearing an open-collar shirt and blazer, and carrying what appeared to be a blue cool bag.

He waved to reporters outside the hospital and put the bag in the rear seat of his Range Rover, before getting into the driver’s seat and driving away.

It is believed Anne, a skilled horsewoman who competed in the 1976 Montreal Olympics, was kicked by a horse while walking at her Gatcombe Park estate on Sunday.

Emergency services and an air ambulance attended and she was treated at the scene in Gloucestershire.

The princess was transferred to Southmead Hospital by road for tests, treatment and observation.

Vice Admiral Sir Tim Laurence in the driving seat of a vehicle
Vice Admiral Sir Tim Laurence arrives at Southmead Hospital in Bristol (Ben Birchall/PA)

She was accompanied by Sir Tim, her second husband, whom she married in 1992.

On Monday Prime Minister Rishi Sunak and Labour leader Sir Keir Starmer sent her their best wishes for a speedy recovery.

Buckingham Palace said in a statement on Monday: “The Princess Royal has sustained minor injuries and concussion following an incident on the Gatcombe Park estate yesterday evening.

“Her Royal Highness remains in Southmead Hospital, Bristol, as a precautionary measure for observation and is expected to make a full and swift recovery.

“The King has been kept closely informed and joins the whole royal family in sending his fondest love and well-wishes to the princess for a speedy recovery.”

Although the cause of the injuries is unconfirmed, Anne’s medical team have said her head injuries are consistent with a potential impact from a horse’s head or legs.

It is understood the princess was walking within the protected perimeter of Gatcombe Park when the incident happened, and no other individual is believed to have been involved.

Anne’s daughter, Zara Tindall, and son, Peter Phillips, were also on the estate at the time, but it is not known who raised the alarm.

As he left the building Sir Tim shook hands with and spoke to Tony Hudgell, North Bristol NHS Trust’s director of operational estates and facilities.

Mrs Tindall later arrived at Southmead Hospital. An Olympic horsewoman, she arrived by car shortly after 4.15pm.