It may depend how big your boxes are - I shipped two small boxes from Albuquerque to my house in Bristol back in August with USPS. One contained a few clothes and the other one had books and papers - they were quite heavy (about 50 lbs in total) and cost me about $200 to ship them. USPS was the cheapest way I could find to ship - UPS/FedEx would have charged me well over $500 - but they will only allow boxes with total dimensions no bigger than 80 inches.
However, since they have now stopped ground shipping with USPS, you have to pay for 6-10 day airmail delivery, which costs a lot more
. It's pretty annoying because you can send boxes from the UK to the US for pretty cheap, using the 6-week ground shipping, but you can't do it the other way around (US to UK) anymore.