This could be challenging but it can be done. First you need to find out the nearest Shipping yard/port in London. You need to make sure who ever delivers the car to port has the Title and Bill of Sale with all your information on it.
From past experience I shipped car to and from Finland because it so much cheaper, but you might need to find a tow truck to deliver it from London to Finland.
Also where are you going to be shipping it, do you live somewhere next to coast. If you live in west it might be easier to ship it to Jersey and again ground transport it to west coast, because to directly ship the car to West coasts is additional $1500.
Be ready to spend a good chunk of money, my estimate somewhere around $3000. You also want to make sure the shipping company offers insurance for the full price of the vehicle purchasing price, because a lot of accidents happens during the shipping process and sometime the loading people are careless.
If you be more specific from where to where you shipping it be a lot easier. Hope this helps, feel free to ask any questions.