It followed the Act of Settlement, whereby the descendants of the Electress Sophia of Hanover and her heirs were declared to be in the line of succession to the throne.
However, Sophia was of German citizenship. This Act naturalized her, and the "issue of her body", as British subjects.
Thus, descendants of Sophia born after the act was passed could claim to be naturalized British subjects. However, the Act lay dormant until, soon after World War II, Prince Ernst Augustus of Hanover claimed British nationality on the grounds of being the issue of the Electress Sophia's body. The claim was rejected twice by the courts but finally allowed by the House of Lords (Attorney-General -v- HRH Prince Ernest Augustus of Hanover [1957] 1 All ER 49). The effects of the 1705 Act had been complicated slightly by the Royal Marriages Act 1772, which included a proviso that the marriages of certain descendants of King George II would be null and void unless the consent of the Crown had first been obtained. This does not apply to the descendants of Princesses who have married into foreign families and, as most of George II's descendants were through the female line, the restriction has a limited effect.
Although the Act was repealed in 1949, it is still thought that some descendants of Sophia could lay claim to be a British subject.