Simon, It's been a long time since I studied Technical Drawing, but I seem to remember how to unfold a conical shape.
Draw the circle equal to the top diameter
Draw the truncated cone shape, which is the front view of the basket
Project the sides down to find the intersection
Draw two circular arcs, centre at the intersection, radius top and bottom of the basket.
Divide the circle into 12
set compasses to 1/12
Step 12 around the top arc
Join last point to intersection
The resultant strip is the correct shape but needs extra material for sewing.
You can have the skippy if you pm me your email address