I went to the Piper day at Duxford yesterday:
I was approaching the runway in use (24) from the NE exactly on runway heading. I tuned to Duxford Info 15 miles out once Lakenheath had dumped me to hear that the circuit was frantically busy.
At 10 miles I called and asked if there was any chance of a straight-in to 24: (principally because, since there are no overhead/deadside joins at Duxford, to join downwind would have meant flying past the airfield to the south outside the circuit and perilously close to Stansted's zone and doing a 180 and joining downwind: a good 5-8 mins extra flying.
As it happened I was asked to report 4,and 2 miles to run, by which time the circuit was clear and I got my straight in (thanks Alan).
Now if the circuit had been busy I would willingly have joined downwind, so if you don't ask you don't get even if initially the circuit appears busy.
Safe flying
Cusco.