The possibility for getting insurance for 1 week and the cost will vary depending on the insurance company and state in which you are purchasing the vehicle. Generally to get auto insurance most states will require the vehicle be registered. It might be possible to obtain tourist registration or temporary export registration for the state you are in.

I would suggest contacting the company that will be shipping your vehicle to Europe. They most likely deal with this situation on a regular basis and will be able to tell you how and where other shippers were able to obtain such auto insurance as you need.

Don't Drive into Trouble is an news article regarding insurance once you get back to the UK. We also have many other news stories that would likely be of interest to you.