The white Mercedes Citan was taken from Cross Street, Bridgtown, at around 5am.
The vehicle was locked but the offender smashed a window to gain entry, officers said.
Now police have launched an appeal after the van was last seen on the back of a low-loader heading towards Willenhall.
Anyone with information is asked to call Staffordshire Police on 101 quoting log number 243 of July 25.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org