I can tell you O2 are unlocking both iPhone 5c and 5s.
Regarding any unlocking though, you have to ensure the phone has been used on the O2 network for them to see, so you have to put the O2 SIM card in and make calls and send SMS too. I always suggest you also put the O2 sim in that you ordered the phone on, so if it was a upgrade phone, you need to get whoever got the upgrade to put there sim in and then for them to request the phone to be unlocked with O2. You also need to allow O2 to see the phone IMEI on the network, so I left my sims in for 24 hours, but i know you don't have to leave them in that long, but it just allows the system to say yes the phone has been on the network.
The key is however to make and receive calls for over 1 min as well, always work I've found if it's been a min or longer.
My 5s was unlocked last year,but I was told I had to pay of the phone plan which I did and no problems, I've just unlocked my 5c and I hadn't paid of my phone plan, again no problems and was done in less than 2 hours as well, which was superb service.
Need Help, Just ask. We are one big Family here in the o2 Forum.
Use iPhone XS Max dual sim, SE, Honor 10, IPad Pro 11, Apple Watch 4 LTE, 100+ Mpbs Barrier and a Record Player.