Please, take your own. You'll find that bikes and parts in the UK are significantly more expensive than in the US, so stock up on spares before you go.
For shipping, you have two options. You can go to your local friendly LBS (Local Bike Shop), and asking them for a shipping box. All new bikes are deliver to the dealers in one, and most of them just crush/recycle the boxes afterwards. These are cardboard.
Alternatively, you can buy a reusable shipping box (plastic), and used that when you want to take your bike elsewhere in the future. The airline will charge you between $40 and $80 each way, even though there are plenty of boxes that now fit within the luggage size requirements. I've gone round and round with gate agents on this one, and have reverted to removing all bike related stickers from the outside, and telling them that it is some other type of equipment. If it fits inside the luggage limits, why should we pay extra just because it happens to be a bike? Anyway, rant over, sorry.
I could go on and on, but you'll be better off just reading this, and checking out the links on the page...
http://www.wikihow.com/Ship-a-Bicycle-Cheaply