Welcome to the Board!
I wouldn't be too worried about sending a quilt to the UK - postal service between North America and western Europe is pretty safe and reliable. Wrap it in something waterproof (perhaps a giant plastic ziploc bag), suck as much air out as you can (with a vacuum cleaner) and then wrap your shrunken, plastic coated quilt in multiple layers of kraft paper or other approved mailing paper. Put the address, and your return address inside the packaging, as well as on the outside. Clearly write the address, and your return address, on the outside of your paper wrapped package, then start with the packing tape - my overseas parcels end up looking like I have coated them in plastic I put so much tape on them!
As far as declaring value you can only declare and insure for replacement cost - which in your case is only the materials you used, unless you've had it appraised. Do NOT put anything like "handmade quilt" on the customs form - you are just announcing to an unscrupulous person that you have an irreplaceable (and therefore potentially valuable) item in your package! Instead put "bedding" or "blanket" or some other generic (and boring) term.
It will cost you a fortune to send it, but I wouldn't be concerned that it will be lost or damaged.
Alison