score:7
Most phones will work automatically in another country, but be forewarned that this does not mean there are no roaming charges or fees. You may even get a courtesy text or phone call to let you know that you are on roaming international data and the fees are quite high. For ATT (at the time of this answer), the cost was $0.15 per megabyte of data used. If you stream a TV show or something you can quickly burn through several hundred megabytes of data in a day and rack up a healthy bill.
To avoid this, you can call almost any carrier and just tell them you're traveling abroad and they can activate a temporary travel plan for you. It may cost $100 or so maybe more or less depending on how much data and phone usage you need, but the plan will last a month and then disappear without disrupting your normal service plan.
Upvote:6
You may want a newer phone.
You'll get 3G service in the UK and pretty much anywhere else in the world on your AT&T iPhone 5, but you can't get 4G service. Even an iPhone 5s/5c would get you 4G service.
The other thing is that AT&T must SIM-unlock the phone before you can use it with a UK-based carrier. They should do this free for the asking if your contract is up, or if you inform them you are traveling out of the country.
With those caveats, you can certainly use your iPhone 5 in the UK with the carrier of your choice -- even AT&T, if you can convince them to give you competitive roaming rates (which may be unlikely).