That's right.Insurance companies cant increase your premiums due to your diabetes otherwise it's discrimination which is illegal.The DVLA have issued your licence so your deemed fit to have a licence...PERIOD!
I'm T1 and only pay £144/yr for a Jag XJ TDVi twin turbo and I got £27 cashback off that (see below).
An awful lot of other factors effect your premium including...
Car;
Age;
How long you've had a (full) licence;
Postcode... (if other people in your immediate postcode have claimed it can effect your premium as you're deemed to be in a more "at risk" postcode);
Occupation;
Mileage;
Excess (increasing your excess typically brings your premium down);
Use;
The list goes on.
Good luck,have a shop around and remember you can reduce the overall cost to you by buying online via cashback apps like Topcashback,Quidco etc
Go to the Moneysavingexpert website to see which comparison sites to use to cover the vast majority of insurers and then when you get a suitable quote but it via one of the csshback sites to save even more,
No disrespect but being a little bit savvy and spending a littls bit of time and it'll save you £££s and not just on car insurance.
Good luck