I expect your body is still making a lot of inslin, but due to high inslin resistance it is not enough to control your BG after your meals. It is possible the inslin level your body is making is higher then someone without diabetes, but as your pancreas is working "full out" all the time the inslin level may change little over the day. A cpeptrade test would comfirm this, but hard to get for T2 on NHS.
In a person without diabetes the background level of inslin is very low, then when they eat a meal their pancreas very quickly releases a short burst of high level of inslin - this is called "first inslin responce" and is often stated in research papers as an increase in rate, not obsolete level. This short lived high level of inslin is responsible for removing the glocose that gets added to the blood from the digestion of carbs in the meal. Mostly this high inslin level gets used by the liver, and never get to the rest of the body - very different from injecting inslin.
In type2 diabetes the "first inslin responce" mostly stops working, hence resulting in high BG increase if a meal contrains more carbs then there is enough inslin to convert into fat. (The glycogen stores are normally nearly 100% filled in a person with type2 diabetes unless they are eating a lowcarb diet)
The level of carbs in the meal mostly determines how much the meal will increase BG however protein also increased BG a little, so even if a meal has no carbs an increased level of inslin is needed by the body to control BG. It is not possible to predict if your body can provide the level of inslin needed for a carb free meal, without you doing careful experiments, monitor your BG and being very aware of the risk of hypos.
It is even possible that your meal time inslin reduced how much inslin your pancreas makes over the few our after the meal to below the level the pancreas makes while you are not eating.