Your phone will work fine. You should contact your provider to get the skinny on their overseas call and data charges though. You may find that getting a pay-as-you-go sim when you get to the UK may be a cheaper bet (I recommend Giff Gaff sims for such purposes) but to do that you will need an unlocked phone (ask your provider). If you have trouble getting it unlocked by your US provider (I hear some get very weird about that) any UK third party phone repair shop should be able to unlock it for cheap.
Please note that you will not get LTE on a US phone in the UK. Also, outside the US terms are different: 3G=H & H+ (covers 4G in US terms) and 4G=LTE. So, if getting a Giff Gaff (or some such) payg sim, don't buy any 4G data bundles and stick to 3G ones for H and H+ speeds which is the max your phone can handle in UK/EU.
Also, remember that the EU wide emergency services number is 112, not 911 (each country has their own, in the UK it's 999, but 112 is EU wide (inc. UK) for the same thing so just remember 112 and you won't go wrong wherever you find yourself). Keep it in your contacts.
Just noticed you're from Arizona. In the UK water has a tendency to leap at you, unbidden, from the sky at regular intervals even in the summer. I advise you seek out a rain coat with good pockets for your phone, this is used by locals to place over regular clothes and water sensitive gadgets for protection. Ask a New Yorker to show you how. Welcome to Britain, please wipe your feet.
Facebook
Twitter
Instagram