I have a corduroy Pittsburgh Kilt. While I'm happy with the kilt, I don't think corduroy is the best material for the job. Corduroy has a good memory: if you sit down then stand up, the kilt keeps standing up. In short, wear it with a sporran.

A corduroy UK might be a different story, though; they tend to have thicker, narrower aprons and might not have the same problem.