Here in Norway, usually, if you are cleared for an touch and go, you have permission to fly the circuit, land, take off, turn crosswind and turn downwind.
If I was on downwind and the tower was busy, I would just continue on an extended downwind, and turn base and then a long final when I was cleared for another touch and go.
If extended downwind is not possible due to terrain or other traffic, I think I would have started orbiting on downwind and waited for contact..