As I noted in the earlier post linked above, most of it comes through intermarriages between Islamic and Christian dynasties in Spain:
Anyway, she [Queen Elizabeth II] apparently doesn't just have just one descent from the Prophet, but multiple lines of descent through several of his children and through several of QEII's own rather varied ancestral lines. Here's one version of her several lines. There are lines from the Prophet's daughters Ruqayya and Umm Kulthum, and a couple of lines through his grandson Hussein (so she could add "Sayyida" to her royal titulature), one of which also passes through the line of the Shi‘a Imams to the 10th Imam (and a sister of the 11th), and yet another through Hussein's brother Hasan (so she's also a Sharifa), and some other variants of these.
The key is that several descendants of the Prophet married into the Umayyad Caliphal house, and when the last Umayyads fled to Spain (al-Andalus) in 750 AD they carried several Prophetic descents with them. The usual intermarriages of daughters and sisters of the Caliphs with various local rulers in Spain eventually included some marriages with local Christian rulers, which in turn put the Prophet's DNA into some of the local dynasties of what became Portugal and Castile, and also into the Hapsburg line. Given all the usual intermarriages, she ended up with multiple descents, some coming through Edward IV, but others coming in through various German and other houses later on, the latest through Mary of Teck, wife of George V and the Queen's grandmother.
And that is the extent of Royal Wedding coverage in this blog.