Bear in mind that depending on where you live, a lot of your US furniture might not fit either up the stairs or in the rooms of a British residence. A California King bed, for instance, might totally overwhelm most British bedrooms and, if you're going to be living in an older house, you might end up having to take out the windows of the room to get the bed in or maybe that won't even work. A large sectional couch might not fit either. There is perfectly lovely furniture to be found at all prices in Britain that will be better scaled to living conditions.
Your electrical appliances - TV, lamps, etc., won't work anyway, at least without at the minimum rewiring.
I DID ship most of my books and personal items over when I relocated to Sweden, because I think you need a few items around that are familiar and comfortable to help with any move.