I just read that he did say that he was sleeping at the time. So would he have been able to change his clothes and get there within six minutes?
Quite possible, I think. Commercial Road ran across the top of Berner St (about 130yds), and no. 100 was at the top of Batty Street (another 40-50yds). So no more than a 2 minute walk, or 18 seconds for Usain Bolt.
I'm not sure how long exactly it would take a Victorian gentleman to get dressed but 4 minutes sounds plausible. Especially as his assistant Johnson estimated he arrived 3-4 minutes before the doctor.