I used Stevens International from the US to UK, and they were terrible. Other people have mentioned they had good experiences with them, but I definitely didn't. My shipment, which I was told would take four to six weeks, took over five months. I moved at the end of May, and everything arrived in early November, in terrible condition.
For a small move (no furniture), I'd recommend looking into the Royal Mail. You can find out the cost on their website if you have your box's dimensions. I used them from the UK to Canada a month ago for seven medium-sized boxes, and everything arrived in just three days (was told it would be four days). In fact, when we arrived, we had slips waiting for us to pick up our boxes at the Post Office. It was around £350 for everything, which was far less than any other method I looked into.