How would you outline how you sell your services? What are your complementary strategies to charging more?
If you can, find out how much the middle-man company is farming you out for. Let's say you once did a contract through ManPower for ABC company. ABC company needs some labor, and you did a good job, so they reach out to you directly. You should be billing what ManPower billed your time for, not what you billed ManPower.
This is generally only possible to do through smaller businesses. Big corporations typically have contracts where they require you to go through one of their preferred vendors.