Can I use a UK IPhone in HK?

Buy at apple store instead, they give you options to buy unlocked phones

If you are going to do this you must buy the phone in an Apple store. No other UK provider sells unlocked phones, although some sales staff in other stores will lie about it and say the phones they cell are unlocked.

There are two options available.

1. Carrier Locked (This will not work in HK)
2. Carrier Free ( Will work any where in the world with All carriers)

Also note that iPhones do not carry worldwide warranty.

Yes. Warranty coverage can be denied in any country other than the one where it is purchased. The reason is that Apple does not repair phones in the store; they replace any phone needing warranty service, and send the defective phone to a depot to be repaired and refurbished. Phone models are country specific, particularly with regard to government regulations regarding radio devices. And HK and UK regulations are so different that it is unlikely that a phone bought in either one can be repaired on the other. You might be able to get a screen or battery replaced, but even then the store has the option to deny service.

This is also taken from Apple One (1) Year Limited Warranty

IMPORTANT RESTRICTIONS

With regard to iPad devices with cellular coverage and iPhone devices, the warranty provides service coverage the European Economic Area (EEA) countries and Switzerland. Outside this region, service options may be limited due to technical issues outside of Apple control – for information relating to iPad devices with cellular coverage and iPhone devices please see www.apple.com/iphone/LTE/ and www.apple.com/ipad/LTE/.

With regard to iPad devices the warranty does not provide service coverage in China due to differences in WiFi connection outside of Apple control.

It may be possible but you would have to pay for that. It would not be covered by the warranty.

The following it taken directly from Apple One (1) Year Limited Warranty:

You may obtain service in the European Economic Area (EEA) countries and Switzerland without paying any shipping and handling fees. Outside this region, service options may be limited. If a given service option is not available for the Apple Product in such country, Apple or its agent shall notify you about any additional shipping and handling charges which may apply before rendering service. Shipping and handling charges will not apply in countries where Apple does maintain an Apple Retail Store or Apple Authorized Service Provider (“AASP”) (a list of current service locations is provided at locate.apple.com/uk/en).

You will not be able to get warranty coverage repairs in HK.