There were no Mohammeds and Sajids in Britain at one time.
Indeed there were not. But then at one time there were no Ernests, Fredericks, etc either. 1000 years ago names like Ælfweard ajnd Ælfþryð were common. King Æðelræd II's wife was Ælfgifu.
Things change. No matter how much you may dislike it, and no matter how much you try to stop change by kicking against it, change will take absolutely no notice of you whatsoever.
There were Ernests, Fredericks, Johns, Alfreds and all the biblical names like Luke, Matthew, Thomas, John, even Ezekiel and Ebenezer. But no Mohammeds... that name is distinctly foreign.
"Foreign", eh?
Ernest -
Derived from Old High German ernust meaning "serious, earnest".
It was introduced to England by the German House of Hanover when they inherited the British throne in the 18th century, though it did not become common until the following century
Frederick -
English form of an Old German name meaning "peaceful ruler", derived from fridu "peace" and rih "ruler, king".
The Normans brought the name to England in the 11th century but it quickly died out. It was reintroduced by the German House of Hanover when they inherited the British throne in the 18th century.
John -
English form of Iohannes, the Latin form of the Greek name Ἰωάννης (Ioannes), itself derived from the Hebrew name יוֹחָנָן (Yoḥanan). This name was
initially more common among Eastern Christians in the Byzantine Empire, but it flourished in Western Europe after the First Crusade.
Alfred - Means "elf counsel",
derived from the Old English name Ælfræd, composed of the elements ælf "elf" and ræd "counsel, advice".
And as we all know, Old English, and its names developed from the languages brought to Great Britain by Anglo-Saxon immigrants in the mid-5th century.
Luke - English form of
Latin Lucas, from the Greek name Λουκᾶς (Loukas), probably a shortened form of Λουκανός (Loukanos) meaning "from Lucania", a region in southern Italy. The name became common in the Christian world (in various spellings). As an English name, Luke has been in use since the 12th century alongside the Latin form Lucas.
Matthew - English form of
Ματθαῖος (Matthaios), which is the New Testament Greek form of Mattithiah.
Thomas -
Greek form of the Aramaic name תְּאוֹמָא (Teʾoma) meaning "twin". In England the name was used by the Normans. (The Normans were invaders, in case you'd forgotten).
Ezekiel - From the
Hebrew name יְחֶזְקֵאל (Yeḥezqel) meaning "God will strengthen", from the roots חָזַק (ḥazaq) meaning "to strengthen" and אֵל (ʾel) meaning "God".
Ebenezer - From the name of a monument erected by Samuel in the Old Testament,
from Hebrew אֶבֶן הָעָזֶר (ʾEven Haʿazer) meaning "stone of help". Charles Dickens used it for the miserly character Ebenezer Scrooge in his novel A Christmas Carol (1843).
Currently the name is most common in parts of English-influenced Africa, such as Ghana.
So which of the names in your list did not start out being "foreign"?