When I moved, I stored all my stuff in a rental place. I kept my car at a friend's house. And I had my brother and sister rifle through my things to take out EVERYTHING they wanted that was electrical. I planned to sell my car and ship the rest once I officially decided the UK was for me.
Well, the car didn't sell, and not many things electrical were taken out, so I ended up having to ship far more than I ever planned.
As far as pricing, I found this good indicator online...if you store in a unit within the US:
U-Store ItHowever, I think you were really asking for UK rates. When I moved across I was stunned by the lack of storage units. (Well, in Florida, they are on every corner, so it was a bit of overkill.) We did end up storing for six or so months and I wasn't thrilled with the price, though I can't recall it now. We found our storage place through our local moving company ("removals"), so I imagine that's a main route people go through for storage...ie, look for adverts for removals and ask if they do storage.
The overseas moving company we used was Pickfords, and to ship my car and a full three-bedroom house, including insurance, this ran around £2,500.
I note on their web site they do offer storage, though I can't immediately see rates, their other info on moving seems very helpful.
Pickford's storage