I have bought an unlocked, used iPhone 4s from my friend, but it doesn't work with my SIM

I have recently bought an iPhone 4s from my friend. I am with Tesco Mobile and she has got this phone as a part of a contract with 3 (UK privider). Knowing about the problem with unlocking them, we decided to ask 3 to unlock it. They agreed and all seemed fine, and after some time they have sent an email confirming it's unlocked.

In the meantime I requested a new tesco mobile SIM card that goes with iPhone 4s (as before that I had a standard size SIM). Initially I wanted to order a SIM swap of my phone number to that new SIM, but I haven't done that yet as I didn't want to end up without a phone for a couple of days (as we didn't know how long the unlock will take). So I only have this inactive micro SIM with tesco mobile.

We put the SIM in the iPhone and followed all the steps (resetting to factory settings and connecting to iTunes), but I still get a prompt that my SIM is not supported. We called 3 and they claim that the phone is already unlocked on their side.

What can be the origin or the problem? Can it be because the SIM in the phone is inactive? Should that matter? Or are there steps I could have missed? Would going to Apple Store help?