Thanks for this eye opening question, the answer to which I had to find doing various searches despite being a member of the Institute for a long time.
Section 18 (4) of the Chartered Accountants Act 1949. It says "The annual accounts of the Council shall be subject to audit by a chartered accountant in practice to be appointed annually by the Council"
Council is a body of people that is elected annually by the members. It also has some people appointed by Central Govt. What I understood from my further searches is that, one of the various committee's of the council called Audit Committee does the selection process of auditors and recommends to the council for appointment.
So it is like Members (CAs) elect the council and council appoint the auditors. Hope your query is cleared.