Fernando Gomez, 35, from Hackney in east London, had been in intensive care for several days but his condition deteriorated overnight and he died around lunchtime, the Homerton University Hospital said.
Health Protection Agency (HPA) staff have sealed off his flat and are due to inspect his workshop this week to test for further signs of the disease, which can cause a skin infection or, as in this case, be inhaled into the lungs.
Seven people who had been in the room where the animal hides were prepared have been given antibiotics as a precaution, but HPA officials said no-one else has developed symptoms of anthrax.
Anthrax is a highly contagious infection that usually only afflicts livestock, but can be transmitted to humans who handle or eat infected animals. Anthrax inhalation is very rare, and is not contagious.
Officials stress there is little risk to people playing animal hide drums, only those making them, and Britain has tough regulations on hide imports.
The last death of this kind in Britain was in Scotland in 2006, when 50-year-old Christopher Norris, who made artworks and instruments including drums, died after inhaling anthrax.
A subsequent report said it was likely Norris died after playing or handling anthrax-contaminated West African drums at a drumming workshop.