Diabetic meals do include carbs. If I were to venture a guess, I would say that low calorie would be your best bet, but comes a point when any airline can only offer so many types of special meals and unfortunately in this case, the specific requirements that you have are not specifically catered by BA and there is a risk that any special meal will include some products you will prefer to avoid and may need to skip. Unfortunately, the current lack of choice of starters makes the option of a regular meal even worse for you than in usual times, hence my suggestion that low calorie might (with no guarantee) be the closest to what you need.

Description of all BA special meals is on the website by the way (here: Special meals | Food and Drink | British Airways) so you can have a look and see if there is any which you trust more than others.