As far as I know, there has not been a consensus on his death. I've been mostly interested in his sisters in my readings (Mary I: England's Catholic Queen by John Edwards: Yale University Press; there are many books about his sisters), but from what I've read there are three theories that have a good basis in modern medicine:

1. Tuberculosis

2. Bronchial Pneumonia

3. Poisoning

Medical diagnoses from historic chroniclers is somewhat difficult. By the time of Edward, chroniclers had become much better at describing diseases (less "the humors were out of balance") so that we can now get a general diagnosis in the present, but without an autopsy, it is difficult to say what exactly killed him. From some of the descriptions I've seen (I have not come up with a source talking about the ulcers, if you have a source that would be great), I think it is more likely that it is a bacterial infection, so either tuberculosis or pneumonia. It could have also been an inhaled poison, but the up and down nature of his illness makes me believe that it was more likely an infection.

From a biological perspective, it is hard to pin down just one possibility without doing a swab of his bronchia (not exactly possible 500 years after the fact). The sources I've come up against say that it was mostly the lungs at first followed by the swelling of the legs, which leads me to believe that the swelling is a complication of the original disease and not an actual symptom of the original. There are lots of reasons for edema, including congestive heart failure, infection, etc. All of which would be caused by all three theories.

Really, it is hard to determine cause of death unless the royal family allows the exhumation of his body, and even then any findings would be highly contested and the accuracy of them would be perpetually called into doubt.