Carrier unlock of an iPhone 5S

I wish to leave my carrier, T-Mobile (UK), and move to Three. I have a PAC code and have given 30 days notice as my contract expires next month. My iPhone 5S was purchased from Carphone Warehouse SIM Free (unlocked) and I then put my T-Mobile pay monthly SIM into it.

T-Mobile claim they cannot unlock the phone since they did not sell it to me and to contact Carphone Warehouse.

Carphone Warehouse said they do not unlock phones since it requires the carrier numbers and therefore only T-Mobile can unlock it (they also recommended I contact Ofcom if T-Mobile refuse)

Upon contacting T-Mobile again I was informed that my iPhone is only locked for theft prevention and I can put a new SIM in and do a factory reset and use the new carrier's SIM (Three).

Is this correct or are T-Mobile still trying to escape the issue?