Catching up from this post, everything has changed.
The original phone hasn't found its way back to O2, and after a little convincing they accepted that this really couldn't be my problem (since they sent it to the wrong place). I have been ordered up a new phone and SIM card. This succeeded eventually by ordering the phone to our buildng number and sticking a note on it to tell the courier which flat to look for! I now have the SIM card - was addressed wrongly but the postman knows where I live - and it is working in an old handset, but the phone has been held up. Apparently there's been a recall on the chargers as they are exploding (!), and the warehouse has to inspect all their stock before they send it out. I still await...
On the plus side, I figured out why my address wasn't working. The system (including Experian, the credit reference people) has our postcode wrong. The other flats on this stair are under the correct postcode, while ours is under the one for the other end of the street. Now I know.
Modern technology. I complain about it, and then I jump through all these hoops to get it.