I think the collective minds of PPRuNe have come to the right answer!
Approach "cleared" you to join the circuit at left base. The Tower didn't tell you to "call before turning final", so you can do that, too.
I fly at an airfield with Approach and Tower, and it's not at all unusual to turn finals and be told "continue approach". Usually, I can see the aircraft ahead or on the runway - either about to turn off, or about to takeoff. Sometimes, I can't see any reason for not getting the landing clearance - then the little tractor nips across the runway.
Even though we're all supposed to know the answer to this one already, I feel happier now and know what I'll do if it happens to me. Thanks for the question!