Please clarify that the diameter fo the crankshaft is 5/16".
Keyways are normally designated by their width, which has some, but not a 1:1 correspondence, with the shaft diameter into which they are cut. Hence you need to tell us what size keyway you want to cut. Search for 'British Standard shaft keyway' or similar and you will find dimensional information.
The broach is used for the pulleys. The keyway in the shaft can be cut by numerous methods, probably a slot drill is easiest, but you can chain drill, chip out some material with a cape chisel and finish with a file if you want.
Let us assume the desired keyway is 1/8". You can then search for "1/8" keyway broach" and select a supplier that meets your requirements. You will need a bushing and shim or two to complete the setup as well as something with which to push the broach. Check the equivalent or closest standard metric size as that might be cheaper than an imperial one.
If you want to buy it, the key itself is made of 'key steel', usually available in 12" lengths.