I recently contacted my travel insurers (I use that which comes with my bank account) with the information I had been diagnosed with T2. They were happy for me to continue to cover me for anything that didn't stem from the diabetes (apart from the usual hazardous sports exclusion etc.). As I am not yet on any medication and the GP considers my glucose levels well controlled, I was happy with that. Insurance companies are in the business of not paying out and will try hard to maintain this, so if I had not declared and, for example, broken a leg in a non-diabetes related accident, I suspect that I would not be covered.
Have they actually said they are covering you for non-diabetic incidents only? Does that mean they will not cover you for anything diabetes related? If that is the case, I would want clarification on that.
If, for example, someone with that insurance policy condition/exclusion, were unfortunate enough to suffer a heart attack or a stroke, say, I wouldn't like to be the one having to fight my corner as to whether diabetes contributed to such an event.
At the point of claim, insurers have a slightly conflicting duty of care, in that they should pay all calid claims, but at the same time, must protect their commercial shareholders by resisting claim payouts, where there is a reason to question it. If there is doubt, or ongoing discussion, there could be delays settling bills, which isn't what one needs when one is under the weather.
I advise you ask your insurer to confirm you are completely covered, under the normal policy conditions of the standard policy. If not, I would advise you consider shopping around. Myself and many others have found we are covered as if a "normal person", with no exclusions (aside from naked hang-gliding, surfing with sharks or other considered hazardous pursuits. Nor have I ever had a premium loading.
It may be worthwhile looking at your policy documents to find the underwriter. A couple of the big banks underwrite their own cover, with the balance usually using AXA, Aviva or Legal and General.