Having shipped a lot US > UK the best is Global Priority Mail in the flate-rate box (approx 12x6x2"), which is about $12. This usually takes 5 days and arrives by Royal Mail in the UK. The fees for collecting duty are reasonable.
Airmail Parcel Post is better for larger items that don't fit the box or heavier items and takes about 2 weeks and arrives by Parcel Farce^WForce who either smash it up or abandon it on the doorstep. I there are import duties to collect they ransack your wallet for their "fees".
Gareth