The Princess Royal is “doing fine”, Vice Admiral Sir Tim Laurence, her husband, said after visiting her in hospital, describing her recovery as “slow but sure.”
Sir Tim, 69, arrived at Southmead Hospital in Bristol just after midday, entering via the front steps.
He was carrying a large blue cool bag that he said contained “just a few little treats from home”.
He left after lunch two hours later, offering a brief update on his wife’s condition before heading home.
The retired Navy officer, who enjoys a low profile, accompanied Princess Anne, 73, on the 30-mile journey from their Gatcombe Park estate in Gloucestershire to hospital on Sunday evening.
Princess Anne’s daughter Zara Tindall was also pictured on Tuesday afternoon arriving at the hospital to visit her mother.
The Princess was transferred by ambulance after sustaining head injuries and concussion, having apparently been struck by a horse.
Asked by a wellwisher how the Princess was, Sir Tim said: “She is recovering well, thank you.
“We are both profoundly grateful to the medical team and hospital support staff for their expert care – and to the emergency services who were all so wonderful at the scene.
“We are both deeply touched by all the kind messages we have received from so many people near and far. It means a great deal.”
Zara Tindall, the Princess’s daughter, arrived at the hospital shortly before 4.30pm wearing a denim shirt, denim shorts and sunglasses.
Mrs Tindall, who lives on the Gatcombe Park estate, was in the vicinitywhen the accident happened on Sunday evening.
It is thought that due to the concussion, Princess Anne is suffering from temporary memory loss, meaning that the specific details about what happened have not yet been ascertained.
There were no apparent witnesses to the accident.
However, her medical team said her injuries were consistent with potential impact from a horse’s head or legs. Palace sources said she was awake on Monday.
The Princess, a former Olympian equestrian, was walking on her estate when the incident occurred.
An air ambulance was scrambled but after being treated at the scene, the Princess was taken to hospital by road.
Local residents also saw a police helicopter circling. No one else is believed to have been involved.
Southmead is the largest hospital in the South West and has a specialist neuroscience unit. It is also home to the only adult major trauma centre in the Severn Major Trauma Network, working alongside six other units in the region.
The King and Queen, the Duke of York, Duke of Edinburgh and the Prince of Wales were informed on Sunday evening and the monarch is being kept updated, having sent his “fondest love and well-wishes” to his sister.
Buckingham Palace said the Princess was expected to make a “full and swift recovery”. She is expected to be discharged from hospital later this week.
A spokesman said she was “in a comfortable condition” and was being kept in hospital as a precautionary measure for further observation.
Rishi Sunak, the Prime Minister, and Sir Keir Starmer, the Labour leader, broke away from election campaigning to send the Princess their best wishes for a speedy recovery.
The Princess had been due to fly to Canada at the end of this week but has now postponed the trip on doctors’ advice. She sent her apologies to those who may be inconvenienced or disappointed as a result of her cancelled engagements.
She will also miss a state banquet held in honour of the Emperor and Empress of Japan’s visit on Tuesday evening.
It is not the first time that the Princess has lost her memory following an equestrian accident.
At the 1976 Olympics, she suffered a bad fall at a jump as her horse, Goodwill, became stuck in a boggy mud. She later described her memory as “almost non-existent for that day”.
The Princess, often dubbed the hardest-working member of the Royal family, is known for her no-nonsense approach and her commitment to royal duty.
At Trooping the Colour earlier this month, she was pictured expertly keeping her horse under control when it appeared agitated.
The Princess won the individual championship at Burghley in 1971, and was voted BBC Sports Personality of the Year.
In 1976, she took part in the Montreal Olympics as a three-day eventer with the British equestrian team.
The Princess survived an attempted kidnapping in 1974 when a gunman tried to abduct her and then-husband Captain Mark Phillips as they were driven along The Mall to Buckingham Palace.
She kept her cool, and when the gunman, Ian Ball, told her to “come with me for a day or two” because he wanted £2 million, she replied it was not “bloody likely, and I haven’t got £2 million”.
