I have asked for an unlock for my iPhone from threeUK?

My current network is 3, I want to unlock my iPhone to use my other sims, but Will I be able to use my threeUK sim again on my iPHone? Will I need to keep unlocking my iPhone if I want to keep changing sims?

No need to unlock your phone again once it has been factory unlock. Once your iPhone has been iPhone Factory Unlock, you will be able to use it any carrier. You can use three UK sim again if you like.