This is actually true:
"In 1023, Abu al-Qasim Muhammad ibn Abbad became the ruler of Seville in al-Andalus. He was formerly a qadi (judge) appointed by the Caliph of Cordoba, but seized power and formed his own dynasty, the Abbadids. He was a descendant of Muhammad through his daughter Fatima and grandson Hasan ibn Ali.
In 1091 the Almoravids from Morocco invaded Muslim Spain, and his grandson Al-Mu'tamid ibn Abbad lost his throne. His daughter Zaida fled north and took refuge at the court of King Alfonso VI of Leon. She became his mistress - the king was already married, but his wife was bedridden with illness. Zaida later converted to Christianity, took the baptismal name Isabella and - once the king's previous wife died - married him, bearing him three children that we know of.
In 1352 Maria de Padilla, a descendant of Zaida and Alfonso, became the mistress of King Peter 'the Cruel' of Castille. They had four children - two of the daughters married sons of King Edward III of England. It is from Isabella of Castille and Edmund, Duke of York that the current Queen of the UK is descended."
They also claim to be descended from King Arthur though that's ironically more of a stretch.