Technology giant HP is one of the many companies that started from shedlike premises. You can still visit the HP Garage today (pictured here in 1939 when Hewlett-Packard was founded) as it is California Historic Landmark No. 976 — Birthplace of Silicon Valley. HP have preserved it at 367 Addison Avenue, Palo Alto, and although it's not open to the public, you can see it from the pavement/sidewalk. There's a huge amount of detail and numerous articles about the garage at the HP site here. Thanks to Cathy Dobson for alerting me to this.
Closer to home (well, my home), is Herbert Frood's shed at Combs in the Peak District. In his garden shed he designed 'brake shoes' for horse-drawn cart wheels from hair and bitumen. He called them Ferodo and made a fortune thanks to commissions from, among others, the London General Omnibus Company and the army who fitted them to their tanks.
The hut is still preserved, on the works bowling green of the factory he moved out to when the shed got too small. More information from Peakland Heritage here.