To get a place before you come over, you either have to take one sight unseen (not recommended) or make a special trip a month before you move and spend a few days looking around (and if you don't find a place before you have to return to the States, you'll be really frustrated that you didn't plan for a couple more days to look). So it's up to you, but that's a lot of extra expense and frustration that you could easily avoid.
I would recommend you book a b&b or serviced apartment for a week for when you first move here, and you can use that address or your work address (if you have one, this is best) for the shipping address. Also, get a travel cell with a UK number (or buy a regular pay-as-go when visiting the UK) before you move so that you will have a UK number to give the movers and estate agents. It takes a few weeks for your things to arrive from the States, and if you don't have a place by then, they can put your things in storage briefly. But unless you have some special requirements, you'll surely find a place by the time your stuff arrives. Look online and line up some viewings and estate agents before you arrive, and you'll find something within that first week. It's possible it won't be available immediately and you may have to wait a week or two to move in, so I'd make sure to have found a couple of back-up lodgings you can call if the one you're staying at isn't available for an extra week or so. And you may want to wait to move in until your stuff arrives, anyhow, if you don't want to camp in an empty apartment. We got an unfurnished apartment, but moved in before our furniture arrived because we brought an air mattress and battery-operated inflater in our luggage (these things would cost you MUCH more in the UK).