Sandringham House, in Norfolk, was the first home of Queen Victoria's eldest son, Prince Albert Edward (to become King Edward VII) and his wife Alexandra in 1862. Later, King George V would start the enduring tradition of the Christmas Message in 1932. The Royal Family spend the Christmas holidays (until February) at Sandringham, but when they are not in residence it is open to the public. It is the private property of the Royal family and not part part of the Crown Estate. The original hall was built around 1771, but was completely rebuilt in 1870 in a variety of styles.
the fountain and fish pond are part of the kitchen gardenlink showing the plan of the gardens
these "art colour" postcards are from an original watercolour by J Lindsay, but I haven't been able to find much information on him.
edited to add a link to Isabelle's post on the gardens