Is there an issue with the contract management being at one step removed under the PSAA regime, which is perhaps the price for the benefits of centralised procurement?

The local audit framework, the respective roles of the different players, e.g. the FRC, NAO, ICAEW, CIPFA, DLUHC and PSAA, and the nature of public audit means that any contract for the delivery of a code-compliant local audit will be different to a normal services contract.  PSAA (or local bodies) cannot specify the audit work or its depth, and by necessity local auditors are independent once appointed.