No experience on Cowells specifically, but it does look like you are faced with the common choice on such machines: Either remove the spindle from the headstock and the countershaft from the H frame so that you can fit a new continuous belt. Or fit a link belt that can be joined up without having to pull the machine apart.
Fenner brand seems to be the popular choice for link belts, if they come in the right cross-section for your small machine. They are popular among Myford owners, who use a “full-sized” A-section belt. The Cowells may use the smaller Z or ZX series or similar.