Pretty much. But if your mind is completely made up about transferring I would start the process with Three
NOW as they do like to play games depending how long you've been a customer of theirs.
You can Follow the guide here like i did and try to obtain a PAC code either by SMS or in the account settings on your online account or you may need to spend 30-40mins on the phone with their customer support team who will do everything fucking thing under the sun short of giving you a BJ to stop you leaving their network. They wouldnt give me a code online or via SMS so i had to call them.
If you've been with them super long like I have. I was with them almost 15 years. They will try and match whatever offer youre switching to on their competing network. For instance. I was paying £15p/m with three. I switched to lebara which is something silly like £6.90 and only when I was asking for a PAC code did they really try to do anything to keep me as a customer.
But for me the move was very personal... Having basically grown up with the network. Their network service hasnt gotten any better since the day I signed up over a decade ago. No point giving me a £300 Tablet or a £800 phone if the network itself suffers from patchy blackspots and very very inconsistent performance that leaves youtube videos buffering even at 480p.
PAC codes are valid for 30 days. So you'll still have more than enough time to sort your business out with O2, Even if they were to fuck up the process multiple times somehow.
::EDIT::
If its not very apparent. I dont recommend Three at all. One good thing about them is this they are a Hong Kong based network. I have no roaming charges when I go there to visit family. That was the ONLY good thing about three FOR ME.