Hi,
The simple answer is absolutely YES. Almost every insurer will load a life insurance policy for T1's, the amount will depend on the length of the cover required (presumably you want to insure your life for the duration of the mortgage) any complications and the time you've been T1. When we changed lenders part way through our mortgage our new lender (Abbey/Santander) wouldn't continue cover for me but did for my non-diabetic wife.
Insurance becomes harder to get, let alone afford, as things 'progress'. My advice would be to choose your lender very carefully and expect to stay with them for the duration of the mortgage. That way, if you do get sensible cover at a fair price, it will not go up over the course of your loan period. If you do change lenders in the future, insurance may be harder to get and you might even have to factor the premiums into any savings you hope to make by moving the loan.
I should also mention that you don't have to take the life policy from the mortgage lender. You are far more likely to get a cheaper policy from an insurance broker, as lenders will add their fees to the policy price. Of course, life insurance is optional and not a legal requirement for a mortgage offer, but most people do tie a life policy to the term of their mortgage.