Hello and welcome to the Forum.
If the belt is in good condition (not turned to a gooey mess or have lots of bad cracks/splits) other than being broken, some people have good success with using superglue to glue the ends of the belt back together. If the belt appears too slack, then using a sharp blade cut a piece off each end (to reduce its length, ensuring to get a square cut) before gluing.
If it exists the Service manual must be very rare, you can purchase a 3 page schematic and valve voltages info sheet from here -
https://www.service-data.com/section...tant-downloads
From an older Thread the tape deck is a BSR TD4, said to be the same as the TD2 apart from different heads. You can also purchase the TD2 manual from link above.
Very rare to find any drive belt dimensions in service manuals.
The User manual is equally rare as the service manual.
eBay generally can be a fairly good source of old tape recorder spares but little if anything currently showing for the FT1.
Suggest you post a request for the manuals here -
https://www.vintage-radio.net/forum/...splay.php?f=28
David