I shipped three boxes over...for each, I filled out a customs form that the post office gave me. I'm not sure if it was a C3 form or not. It basically asked me to declare what was in the box (I put "used household goods (books, toys, pet supplies)" or some such for each) and asked for my address in the US, in the UK, and where to send the box if it couldn't be delivered to the UK address (we used DF's dad). The insurance we'd purchased for each box was also listed.
Like I said, I don't know if these were C3 forms or not, but my stuff got here just fine, and with no problems - the 4-10 day airmail one arrived 11 days later, and the two 6-8 week surface mail ones arrived at six weeks and eight weeks, respectively.
It depends on how you're shipping things, of course, but if it's through the USPS/Parcelforce, they should be able to provide the necessary form....