The Money Saving Expert website recommends using a web broker, rather than going directly to the well-known courier companies. For their sample package (10kg to New York), this broker came out best:
http://www.worldwide-parcelservices.co.uk/
However, since your package is a smaller weight (and probably going to a different part of the USA) one of the other two brokers recommended by MSE might be cheaper:
http://www.transglobalexpress.co.uk/
or
http://www.pharosparcel.com/
Note though that those services are by air. Your post refers to services by ship but there are actually very few firms that offer such services. That's largely because, on arrival at a US port, the package would then probably still be flown to its final destination anyway, so it doesn't work out much cheaper. For example, Parcelforce Worldwide charge £34.75 for their 'Global Value' airmail service to the USA (for a 2kg package), providing a 5 to 8 day service. Using their service by sea, taking 28 to 46 days, only reduces the price by 55p, down to £34.20.