Just my two cents:
APPLY OR RENEW ONLINE WITH THE US ONE!
I let my US membership lapse in January and naively showed up in Reading last week, ready to sign on the dotted line. Unfortunately, they wouldn't let me. UK trading laws require that Costco limit their membership to bona fide businesses or individuals of certain professions. As an archaeologist, I don't qualify. I checked with a Costco over here, and they assured me that it's totally kosher to renew with the US and use it here - it's valid, and you can use it over here freely. I'm in the process of doing it this way. I'm having my new card sent to my mom, who will forward it to me. Also, it's a tad cheaper to do it this way. I'm a big Costco fan, so this was high priority for me (once I found out they were here). MUCH fewer hoops to jump through in the US.