Obviously you would assign a U.K. geo-location to the .com.uk site
When you have a country code domain such as .co.uk, you cannot assign it to another country - only the UK. The options in WMT are grayed out and inactive
Although it's cool to put content across multi TLD's and rank on each of Google's regional listings, what is not clear is whether this form of duplication can effect your Panda score and get your penalised.
I've worked with several companies who use country-specific TLDs and none of them have seen any Panda problems.