What inbreeding?
Historic inbreeding of the monarchy over hundreds of years... other than that, none.
Queen Victoria, for example, was married to her first cousin, Prince Albert of Saxe-Coburg.
British nobility is multi-generationally intermarried with most European (including Russian) royals.
Princess Alice's paternal uncle, Prince Henry of Battenberg married Princess Beatrice (a daughter of Elizabeth II’s great-great-grandmother, Queen Victoria). Their daughter, Victoria Eugenie of Battenberg married King Alfonso XIII of Spain, and her grandson, the present king, Juan Carlos, married Princess Sophia of Greece & Denmark, whose father was a cousin of Prince Philip, Duke of Edinburgh.
Likewise, Queen Elizabeth's great-great-grandfather, King Christian IX of Denmark, was also Prince Philip's great-grandfather. They are also related several times through Princess Sophia, Electress of Hanover.
Although the royal house of Queen Elizabeth II is Windsor, it is agnatically the senior branch of the House of Saxe-Coburg and Gotha, to which King Albert II of Belgium also belongs. Their common male-line ancestor is Francis, Duke of Saxe-Coburg-Saalfeld (1750-1806). Elizabeth II’s paternal great-great-great-grandfather was Ernest I, Duke of Saxe-Coburg and Gotha, whose youngest brother was Albert II’s great-great-grandfather, Leopold I. Another paternal cousin of both Elizabeth II and Albert II of Belgium is ex-King Simeon II of Bulgaria, who is a male-line great-great-grandson of Prince Ferdinand of Saxe-Coburg and Gotha, himself the second son of Duke Francis and brother of both Ernest I and Leopold I.