I unsure of the correct terminology...having said that, presumably I will need an adapter to covert my US two prong plug to the style used in the UK. Will I also need a 220 to 110 converter too or does my standard power brick handle that task?
The US power adapter is dual voltage so the only thing you need is an adapter for the plug itself.
I would recommend something like the adapter below. It will work in the UK and if you decide to go to mainland Europe at some point you'll have the appropriate adapter.