Definitely sea shipment is cheapest, I am shipping 1.6 cubic metres from Sydney to the UK (a single sea pallet) and it's costing about AU$500 plus unloading/clearing fees. I would expect it to cost something similar, although call around because prices do vary quite a bit. I have used Dockside Freight Services in Southampton a few times for shipping cars to the UK and they are recommended, but it might be easier to start with a company in Seattle itself since it's not something that can be just driven to a port!

Air freight would cost a lot more due to the bulk, the dimensional weight would be about 700kg (sea freight is charged purely on volume). As an example, Aus > UK is about AU$6/kg, Seattle would presumably be less, but still hugely expensive.