I also have mild hypertension. I'm on medication for all these conditions. But I've never had, nor have any family history of cancer, heart disease, diabetes, any sort of breathing problems or major organ dysfunction.
Any pre-existing condition at all can impact your insurability and rates for life insurance coverage.
You are considered "at risk" because you have health issues, even if they aren't life-threatening.
In addition, Depression is a risk factor for suicide, Hypertension is a risk factor for heart attacks, and being on any meds poses a risk of possibly overdosing on them.
You still may have an option for life insurance. Some insurers offer a graded benefit plan, or guaranteed life insurance with lower limits of coverage and no medical examination needed. There may be some health questions for you to answer.
However, if you are unable to find life insurance elsewhere after comparing rates and plans, you may want to look into guaranteed acceptance life insurance.