According to UK AIC 99/2006 concerning "Avoiding Action - Pilot response to ATC; under "Initiation" it says that "with few exceptions the fastest way to initiate a turn or to initiate a pitch angle is to do so manually, applying control-wheel or side-stick inputs, as appropriate, after disengaging the autopilot. Consequent action should be to adjust the power as necessary; in many aeroplanes it will not be necessary to disengage the autothrottles.
Responses to "Avoiding Action" instructions should not be made by autopilot vertical or lateral flight control selectors because, due to the design of this equipment, the turn, climb, or descent that the Air Traffic Controller has requested and expects to see actioned will be initiated too slowly to serve the needs of the moment.
It is recommended that company Operations Manuals contain Standard Operating Procedures for the action to be taken in response to receiving an avoiding action instruction.