Any illness with eating disorders like diabulimia are very difficult for NHS to treat you.
It is very difficult to get into any eating disorder clinic. Very difficult and very few clinics.
The trouble is with any ED Clinic that admits the person is that certain items are banned, and you do get room searches... so items like insulin and pens have to be supervised. Their staff do not know how to handle diabetes as well.
A lot of time is spent with psychologists and art therapists and meals are very strictly monitored. The people monitoring do not have the diabetes indepth knowledge that you specifically need first....
You need help more along with issues around injecting and hiding your actions... but an eating disorder unit which accepts in patients would be unlikely to be able to manage the diabetes aspect.
Please speak to your family first. Take this step first. Do it at a suitable time at a table, not on a sofa... you can do this but you need support from your family. They will help you, they wont understand totally. Nobody can understand the true depths of your thoughts and actions. They may say wrong things, but they are there for you...