If I buy an iPhone 5S in the US, will it still work back in the UK?

I'm going to Utah then to Las Vegas next year with my school on a field trip, and while we're there we get half a day to spend in a megamall, my question is that if I go into the apple store there and buy an iPhone 5S without a sim, would it work if I come back to the UK and put in my Tesco Mobile sim card?

Thanks in advance

Added (1). Ahh, would an iPad work if I was to buy one of those there?

1. Unless you buy the phone off-contract and unlocked (which, for the 16GB model, is $599), then no. Phones are typically SIM locked to their carrier. And the $199 price is with a 2 year contract.

2. IPads are basically the same.

You can't buy an iPhone in a US mall without getting service from a US carrier. And the phone probably wouldn't function fully in the UK due to the differences in data frequencies, You would probably be able to make basic calls, but no network data would work.

This is just a bad idea.

If it is unlocked and has the same GSM Bands then yes.
Just be ready to pay the import tax though.

The unlocked iPhones start at $649, not the off contract ones which are still locked at $599. That is the model you'd have to buy for it to work elsewhere.

Assuming you are going for a Wi-Fi only model, yes. It would work anywhere.

You just need to buy an unlocked one, Wi-Fi works anywhere of course so thats no issue with ipad or iphone. If you want to use celltowers then just get an unlocked one, not one on contract obviously.