The Battenberg family was a morganatic branch of the House of Hesse-Darmstadt, rulers of the Grand Duchy of Hesse in Germany. 
“Morganatic” means a marriage between people of unequal social rank.  So, for instance, when King Edward VIII (reigned January 1936 – December 1936) proposed marriage to a divorced American socialite, Wallis Simpson, this could be seen as a morganatic marriage because Ms. Simpson was not equal in rank to Edward VIII.
In 1917, most members of the Battenberg family in Britain changed their name to “Mountbatten”, an Anglicized version of Battenberg, due to anti-German feeling in Britain because of World War I. 
The House of Windsor is the royal house of Britain. It was founded by King George V by royal proclamation on July 17, 1917, when he changed the name of the British Royal Family from the German Saxe-Coburg and Gotha to the English Windsor, also due to the anti-German sentiment in the British Empire during World War I. 
Prince Philip, husband of Britain’s Queen Elizabeth II, was born in Greece into the Greek and Danish royal families. Prince Philip’s mother was Princess Alice of Battenberg. 
Mountbatten-Windsor is the personal surname of some of the descendants of Queen Elizabeth II and Prince Philip. Mountbatten-Windsor differs from the official name of the British Royal Family or Royal House, which remains Windsor. Among those belonging to the Mountbatten-Windsor grouping are Prince Charles, Prince of Wales, and his son, Prince William, Duke of Cambridge. 
What this means, in the realm of Grigori Rasputin’s prediction about Britain, is that both Prince Charles and Prince William are Battenbergs.
The Globe, a weekly tabloid newspaper available in the United States, had as its cover of January 4, 2010, “Dying Queen Makes William King!” The idea was broached that the Battenberg Prince Charles was to be bypassed in the British monarchy in favor of his son, the Battenberg Prince William. However in either case the next British monarch after Queen Elizabeth II would be a Battenberg.
Anna Anderson, who claimed to be the surviving Grand Duchess Anastasia of Russia, told her authorized biographer, James Blair Lovell, that “Father Gregory” (Rasputin) was “a saint.” The purported Anastasia spoke always of Rasputin in reverential tones. (Further background on Anna “Anastasia” Anderson: Here’s To You, Anna Anderson, Ersjdamoo’s Blog entry of September 22, 2014.)
Lovell remained convinced throughout the final years of his life that Anna Anderson was indeed the Grand Duchess Anastasia. When Lovell describes his private conversations with the woman, he always calls her Anastasia, not Anna. In the mid-1970s Anastasia told Lovell that Queen Elizabeth II is “the last sovereign of England, but one.” 
“What do you mean?” asked the startled Lovell.
“This I know from Father Gregory,” she replied. “It was he who told that when a Battenberg becomes king of England, all is at the end.” 
——- Sources ——-
 “Battenberg family”, Wikipedia, September 23, 2014
 “Morganatic marriage”, Wikipedia, September 23, 2014
 “House of Windsor”, Wikipedia, September 23, 2014
 “Prince Philip, Duke of Edinburgh”, Wikipedia, September 23, 2014
 “Mountbatten-Windsor”, Wikipedia, September 23, 2014
 Anastasia, by James Blair Lovell. New York: St. Martin’s Press, 1991