Which iphone do you have? If you have an iphone 4s or newer, and a company that is willing to unlock it (I had Verizon and know they will, others sometimes won't), you can put a UK sim card into the phone. For about £10 you can get a pay as you go plan that will include a couple thousand texts, a few hundred minutes, and around 1GB of data. You can use data to send imessages to other iphones (even in the US) for free.
Hmmm I have an IPhone 4 and I didn't think it had a sim card. I really don't plan on making any calls and very minimal texts. I just need to have a phone available in case my elderly father needs to reach me in case of an emergency. He doesn't email or do anything techy so I can't just rely on my tablet and email. I'm still researching the best option. Thanks for the idea though!