I always add fresh green chilli to the recipe, which I find gives it a little more body and certainly bite, without affecting the balance of flavours too much. I would certainly recommend trying this.
I appreciate what you're saying Axe. And I understand (more and more so) that people's perceptions of what constitutes a BIR onion bhaji (or, indeed, any other BIR curry dish) varies enormously.
For me, adding aniseed, fresh chillies or potatoes (or lentils, or ajwain seeds) to an onion bhaji takes it away from what I (in my personal experience) constitutes a typical, traditional, BIR onion bhaji.
The moral of the story is, I suppose, "each to their own".....
For me, given the "correct" cooking method (which I think is not too elaborate but simply ensuring the oil is hot enough to cook them throughout and not so hot that it cooks them too quickly, or burns them, and perhaps double cooking them) the main "lesson" learnt is to minimise the liquid content of the mixture (thereby minimising the "mushiness" inside the bhajis).