Changing Attitude has published a lengthy and detailed analysis on the number of civil partnerships of Church of England members reported to it. You can read the whole report here: Changing Attitude reveals results of Civil Partnership Survey.
They report a total of 87 Anglican events out of an English total of 14,084. (UK total 15,672). (That’s 0.6 % of the English total.)
The official national statistics can be found here.