Nobody so far has said what Cabair actually teaches!
The answer to the question is CCAT (well my instructer anyway) teach the turn from downwind to bace should be made when the aim point for the active runway is percieved to be 45 degrees past the wingtip, which is about at the little white house if 22 is in use. However it can become very busy at TC with circuit traffic and instrument approach traffic and pilots are often told to "report before turning base" to avoid conflict. This is all very well but at these times the RT is also going to be busy and getting the "ready base" call in can be difficult causing the circuit to become extended. Once this happens to one aircraft it can take some time for it to contract again. Also some of the solo students near the start of there course may only have 10 hours TT and not quite be up to your level of excelence yet. It is a SCHOOL afterall and we all had to learn sometime.
Never got to fly the DA40 so dont know the speeds but the problems and frequent PAN calls resulting in the deployment on a regular basis of our friends in the big red truck can not be put down to the students. The plastic planes have a very complex FADEC system (some might say a little to complex for its own good) and a caution and warning panel. You cant blame the pilots (it's not only solo students in my time at cranfield I saw as many instructors being followed by the fire engine as solo's) when they get a caution or warning if they take it seriously. I know I would it the aircraft told me that both the little chips controlling the engine were on the fritz. Remember its only a couple of weeks ago that one of these "new" aircraft crashed after the engine stoped in flight.
Just one thing.
In fact I cut in and so did the aircraft behind me and the student ended up as number 3. He was so far out of position that I never got sight of him at all. (scary thought)
Is it not a bit foolish to cut inside someone in a circuit if you cant see them and dont know where they are. I am not saying that you should go on blindly flying downwind but if you did not have visual contact how did you know he may not have already turned ahead of you and you may be causing a more serious conflict. Would it not have been better to ask ATC for his location, if he was way out of position I am sure ATC would have given you a clearance to cut in and everybody would know what was going on including the solo who might have learned not to go that far downwind next time. Just a thought.