It just occured to me that a bad weather circuit is flown at about 500 feet. So if your PPL without IMC has remained VFR, clear of cloud he has to have been flying VERY low to have remained clear of cloud and need a bad weather circuit. Rule 5 then comes into mind as well.
So back to Bose's comment.
I dont think any height "qualifies" as a bad weather circuit - more as I suggested earlier, a bad weather circuit is more simply anything that keeps you clear of cloud. I can think of a few places were the cloud "sits" on top of the surrounding hills. The "normal" wide circuits take you over the higher ground and into IMC - a tight circuit flown sometimes only a tad lower works well avoiding the higher ground. Moreover without splitting hairs 700 feet may be whats needed on the day - but if you have not had experience of doing it before it can seem hard work the first time. These can also be the exact circumstances where there is very broken scud running through the circuit - nothing worse than seeing aircraft occasionally "disappearing" into the scud or flying the usual wide circuit because they cant fly a tighter lower circuit.
Another example - coming out of Biggin today with plenty of CB activity around, a tight circuit avoided the precip whereas a wider more normal circuit would not have done so. So perhaps just a very tight, but not low circuit, should "qualify" as a bad weather circuit if the circumstances call for it.
Bose is right a PPL with IR should not get himself into those conditions in an ideal world - however the reality is different - unfortunately sometimes the planning is poor - pure and simple, and sometimes with experience we might intentionally push the boundaries. A good friend of mine learnt flying flexwings then microlights and finally SEP. He went around the UK numerous times in his microlight. He never did an IMC or IR but he flew superbly in challenging conditions often low level. He would and did push the boundaries of flight in VMC.
Finally, why are a lot of things taught to PPLs. I often wonder what the point of steep turns really is? However, I think a lot of these tecniques combine to significantly improve a pilots aircraft handling. If you are able to fly a bad weather circuit well you can almost certainly handle the aircraft well and that means you are likely to cope with a power on landing or a power off landing well.