I doubt that there would be much of a problem with the apps on it (as you can always replace any US-based app with a UK).
However:
(a) you might need to replace the power adapter, rather than just get a plug adapter. An American Chromebook will be designed to work on a 120V system (supplied at 60Hz). The UK uses 230V (supplied at 50Hz) ;
(b) it will have a US keyboard, meaning that you might have difficulty in typing a £ symbol and find that other keys are in unfamiliar places ;
(c) you'll get clobbered for around £80 in VAT and a customs examination fee when you import it.
It also needs to be remembered that Chromebooks are designed to be used with a permanent internet connection. The tiny 'hard drive' (actually a solid state device) only has a 32Gb capacity (with quite a bit of that being taken up by the Chrome operating system). So you need to be able to store most of your documents, photos, videos etc in the cloud, rather than on the device itself. For that reason a Chromebook is nowhere near as flexible as a 'proper' laptop (unless you're prepared to spend a lot of time hunting down free wi-fi everywhere you go).