After inappropriately beginning a turn to base based on an 'expected' clearance from approach; a B737-300 Captain called the TRACON and learned that controllers had decided to extend downwinds to prevent a growing number of go arounds behind preceding aircraft that were flying company mandated 'stabilized' approaches which caused a loss of separation with the previous 'rules of thumb' used for VMC spacing.

Narrative

We were approximately 14 southwest at 9;000 MSL on an assigned southbound heading for a downwind to Runway 34R at SLC. Flight conditions were day VMC. ATC asked if we had the preceding aircraft in sight. We answered 'yes with airport also in sight'. I incorrectly anticipated the next immediate instruction to be either 'turn left' (for base) or 'cleared visual approach to Runway 34R;' and began a very gradual left turn. The 'expected' radio call was not made by ATC; and my early turn resulted in a course deviation before I corrected back to the appropriate heading. I chose to call Approach Control after arrival at gate and spoke very cordially with the on-duty Supervisor. He appreciated the call and explained that the 'later than expected' turn/visual clearance was because of recent trends. He mentioned that the decision had recently been made to delay the issuing of 'visual clearances' because several Company aircraft have had to go around due to 'Company required' stabilized approach requirements. He stated 'we [Local Controllers] get gigged' if this happens. There were no conflicts with other aircraft.