Also applying to English MPhil at Cambridge! I'm applying to 18th-century and Romantic Studies, hoping to study Swift and Pope in grad school. Fingers crossed!
Thanks for all the advice, and an update: he finally uploaded my letter! Fingers crossed that he won't be as unresponsive when the future deadlines come...
I'm not sure there if there are any "lessons learned" from this experience, other than try to ask letters from local professors if possible. This professor went to teach at another school, and during the first stages of emailing him, there was on average a 10-day gap before he replied. With professors on campus, at least you could go look for them in their offices...much less risk of being ghosted.