It is understood she was admitted to the southwest England hospital, which is a major trauma centre, after emergency services and an air ambulance attended her Gatcombe Park estate in Gloucestershire.
Anne married Sir Tim, her second husband, in a low-key ceremony in 1992.
The Olympic-medal winning horsewoman is expected to stay in hospital until later this week.
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“Her Royal Highness remains in Southmead Hospital, Bristol, as a precautionary measure for observation and is expected to make a full and swift recovery,” a statement by Buckingham Palace said on Monday.
The King was informed of his sister’s injuries and joined the rest of the royal family in wishing her a a “speedy recovery”, the statement added.
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