Search
Help Google to determine the site language and to serve the right page for the users in different countries. Mark up language attributes correctly. Use <html lang="en_UK"> and <html lang="en_US">. Use <link rel="alternate" hreflang="x" /> in page <head>. It’s also important to specify site targeting in Google Webmaster Tools.
Referrers
I believe people residing in UK will link to your UK-targeted site, not US-targeted. And inversely.
User Experience
It’s always a good practice to leave the user the ability to choose preferred site himself.
Advice
Don’t use any redirection plugins. Google advise sounds the same:
Avoid automatic redirection based on the user’s perceived language
(Multi-regional and multilingual
sites).