The letter asks photographers respect Prince William and Kate Middleton’s privacy after “a number of intrusions” by people with long lenses.
It says it hopes “acts of harassment and breaches of privacy” cease.
Norfolk Police confirmed it was distributing letters on behalf of the royal couple.
Prince William and Kate Middleton have been staying at Kensington Palace since the birth of Princess Charlotte on May 2 but travelled to Norfolk on May 6.
The three-paragraph letter from the royal couple’s communications secretary is being distributed outside Sandringham by Norfolk Police.
The letter says members of the Royal Family and their guests “have a more than reasonable expectation of privacy” while in the private estate.
“There have in the past been a number of intrusions into the privacy of the Royal Family which in the main have been as a result of professional photographers using long-distance lenses, not only to observe the Royal Family, but also to photograph them going about their activities on the estate,” the letter says, adding that previous warnings given to photographers had helped the situation.
“The Sandringham Estate trusts that there will not be a need to take any further action other than bringing these points to your attention.”
Anmer Hall, a Georgian mansion, is about 2 miles east of the Queen’s residence and dates back to about 1800, although some parts are much older.
It has recently been refurbished and now boasts a new kitchen and roof.
A garden room and quarters for the family’s full-time nanny – who will also care for 21-month-old Prince George – was also created during the improvements.
The majority of the work at Anmer Hall was paid for by the Royal Family from private funds.
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