I've just used them...am STILL using them, since my stuff is still sitting in Felixstowe, 'awaiting the next scheduled transport to my area.' Apparently, this can take a while. My stuff left Wisconsin on Feb. 4, and cleared HMRC inspection on April 21. Now I'm just waiting, though I suppose some of the delay was down to the holidays.
So, since I haven't received anything yet, I can't speak to the condition of my items. As for extra fees, the container my stuff was in was apparently selected for x-ray inspection, so I had an extra ~50 GBP charge for that. Also, keep in mind that when they quote you a price, it doesn't include the insurance; that took me a bit by surprise.
Overall, it cost rather more than I was expecting, but given the relatively small amount of goods I was shipping (under 50 cu.ft.), it was still the most cost-effective method I found, and I did a fair bit of comparison shopping. If you're moving more stuff (i.e. - an entire household, enough to fill your own container), then other shipping companies might be more competitive.
Also, you said you're moving to England, so this probably won't affect you, but they're not actually delivering to my door. Because I'm in the Outer Hebrides, they're only delivering as far as Glasgow, and I have to arrange onward transport with a local company. So, that's going to be an extra couple of hundred pounds. Probably nothing you need to worry about, but anyone else who's moving to a remote area should keep it in mind, though I doubt any other shipping company would differ in that respect.