When the British took Cyprus, they decided to set up schools for local children. The British considered whether to instruct in English or Greek, and an English classicist thought it'd be neat to teach the children in Greek, so Greek became the language of instruction.
It wasn't just that - until WW1, Cyprus was still technically part of the Ottoman Empire (hence why it was a British protectorate until the Ottoman Empire completely fell apart, hence becoming a straight-up colony), so at that point in time the pragmatic solution was to teach Turkish Cypriots using the Ottoman curriculum and the Turkish language in Perso-Arabic script (then the Turkish curriculum and Modern Turkish using the Latin script after Atatürk attained power), Greek Cypriots using the Greek curriculum and Katharevousa (when not sucking up to Greece's Ancient Greek restorationist fetish amongst conservatives), and minorities (the Armenian and Maronite communities, for example) left to fend for themselves. Any point to change that equation pre-WW1 would not have been viewed all that well, not just in the Sublime Porte but also among Britain's European allies and the Church of Cyprus.
What if the children of Cyprus had been taught in English beginning in 1878, and over time the island became predominately English-speaking?
The system would fall apart, as the Church, various imams, etc. would consider it contrary to their national religious traditions. If the colonial administration was insistent on it, however, it would have to be at least a bilingual or trilingual English/Greek(/Turkish) system, so as to not offend anyone, and would probably be importing, at least in terms of primary education, the
national school model as implemented in Ireland. Probably to make life easier for teachers, if one wanted to go bolder, one could not only put in place a spelling reform for the Turkish version of Perso-Arabic script (probably something like
the Yeni yazim script used for a brief period in the Soviet Union) and loosen up the Katharevousa to accommodate some Cypriot pronunciation and linguistic peculiarities alongside the standard. Secondary education would be a bit of a mess and would probably remain as per OTL until WW1, when it could be possible to change things around towards something more to Britain's liking (and even then it would probably resemble more, say, Malaysia and/or Ireland) thanks to a change in Cyprus' status as a proper colony.
It still wouldn't make Cyprus predominantly English-speaking, but the English spoken in Cyprus would be heavily influenced by the already-existing spoken languages. For example, depending on mother tongue, the English vowel system could be collapsed either to fit the 5-vowel system of Greek, the 8-vowel system of standard Istanbul Turkish, or somewhere in between.
Another big issue would be Turkish Cypriots, who don't want to join Greece and in this timeline likely speak less Greek than they did OTL if English is the primary language of everything (I dunno how many did OTL though)
Supposedly, Greek/Turkish bilingualism was very much widespread on the island, to the point where to this day there are older generations who can still recognize and have some fluency in the other language. There's possible scope for that to continue, especially if multilingualism is reinforced by the educational system.
If a great many Cypriots speak English, would it potentially foster pro-British sentiment and dampen unificationist tendencies? Could Cyprus end up in a similar position as Malta, which wanted to remain an overseas territory of the United Kingdom?
Not sure about dampening pro-enosis tendencies (you'd need something like Greece going Communist for that to happen), but I don't think it would necessarily foster pro-British sentiment. If anything, the desire for independence would still be there, it would just take a different form and even more so if enosis and taksim are not considered viable options.
