My girlfriend just shipped from UK to USA, the folks she used weren't great, but few transport companies are (in my opinion).
But I know they do air freight as well as sea.
Give them a try, but do get as many quotes as you can, they are:
Hartsmere Logistics Ltd
Ask for Mike, and maybe say Charlotte recommended them.
I used a company called Kingstown once, but not sure if they do air shipping.