Hello Mark P
For reasonably short lengths of wire around a metre:
grip the wire at one end in the lathe chuck
Take a piece of hardwood say 300 long, 30 x 20 mm, with a hole in the middle a reasonable fit to the wire diameter
poke the wire through the hole, move the wood up close to the chuck, hold the hardwood at an angle to the wire, say 20 degrees
run the lathe at slow speed
slide the wood along the wire towards the tailstock
What you are doing is to yield the wire while it is rotating
Of course, eye protection, gloves etc.
Jim