It's mine, I tell you. My own. My precious.
I contacted a company who stocks spares for UK payphones, asking them to send me a set of keys to try.
They replied with "That will not be possible" and the following photo.
@Netraven This is the payphone that was installed in public phone boxes across the UK by British Telecom, the nationalised telephone operator.
The wall of keys was for different models than I have here - because I am not supposed to have this phone and they assumed I had made a mistake with the model number...
I've got plenty of locksmith help on the ground, but thanks for the offer!