There are some brief details of the Appointments Committee of the Church of England (and an
out-of-date up-to-date list of members) on the Church of England website here, and I have copied this below the fold.
But much more useful and interesting is the paper GS Misc 963 Appointments 2010-2015 which “provides details about the work of the Appointments Committee of the Church of England and sets out some of the appointments to be made in the quinquennium”. Although dated October 2010 (and presumably issued to General Synod members then) it has, I think, only just appeared on the Elections and appointments page of the CofE website.
There is provision for the establishment of the Appointments Committee both in the National Institutions Measure 1998 and in the Standing Orders of the General Synod. It is, therefore, a Committee both of the Archbishops’ Council and the General Synod and it is responsible for making such appointments and/or recommendations on appointments to synodical and other bodies as the Synod or the Archbishops’ Council require.