The Latin alphabet was going to replace any other system in western Europe. Not because of the church, but because it was a better system then in use anywhere. It is the same system used in Cyrillic, Arabic, Hindi et al.
Individual symbols combined to create the words. Each of those alphabets are directly descendant of the first developed in ancient eastern Egypt for use with the Armies both domestic and mercenary for the distribution of orders.

First the Latin alphabet is better, then it is the same as any other traditional alphabet. Why is it then better, and why should it replace any other scripts?
The runes have the same background as those mentioned above, and have roughly the same major characteristics as the Latin alphabet, so their demise was not due to any inherent lack of something.
Make the English language alphabet be based on futhork in the present day.
Extra points if the sound correspondance is as good as Esperanto.
Extra points if the language is as globally dominant as in OTL.
The first is fulfilled by having learned christian centres of the 500-1000 AD period staying with runes as the proper and only way to write English, and this is continued to the present day.
The sound correspondences could be reasonable if you keep the script up to date with at least developments that are established since 200 years, continually. A problem in this regard are the different dialects, but there is probably no language with a 100 % graphophonematic correspondence, so it is not that much of a problem.
The globally dominant thing is odd. Why would anything else change, just because English is written differently? The Latin alphabet would be less frequent in today's world, but perhaps not by very much except the English influence. There might of course be a landslide of progressive opinions saying that every modern language should use precise phonemic runes like English, instead of those obsolete haphazard Latin letters that can mean anything.
If English stays with runes, then it might give some impetus for keeping runes in Scandinavian, and also for having special scripts for every language, as it was in olden days. Continental Germanic might be lost for runes, though, unless the English have a strong influence there in the early middle ages, which they at least partially had, so it is not a given.