I'm in a similar position, and was wondering the same thing. From what I can see, the only benefit to going with the bank is convenience. I was advised by a friend that it's better to keep the mortgage protection separate from the bank if you decide down the line to try to switch mortgage providers. Though I spoke to a financial advisor lately who didn't seem to think there was much point in keeping the insurance separate, that I wouldn't be saving anything by going through a broker or direct to the life assurance company.
From reading the policy booklets from a couple of providers, I have to say I can't see much difference in them. With the serious illness policies, it seems to be the same list of illnesses, and similar terms in relation to partial payments. I'm inclined to go with the cheapest quote I get unless somebody was to suggest a reason not to.