It's mine, I tell you. My own. My precious.
Do I have the keys? No. Can we pick the lock? Also no.

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.

@jonty aren't these all tubular keys and your phone has a "normal" key?
@nicoduck Correct! They have now concluded that they aren't allowed to sell us a key, but could unlock it for us.
@jonty why aren't they allowed to sell a key? Are they allowed to sell a key to another locksmith? Or if you can get the bitting, I could cut one (I happen to have a locksmith license now and a key cutting machine)
@nicoduck @jonty You need to have a licence for that?
@1000millimeter @jonty In Germany, you can only do locksmiths stuff (for money) if you're reliable (money/tax wise) and don't have a criminal record.
license in that term meas "just" that the administration registers your business and doesn't decline the application.
@nicoduck @jonty And you do that as a hobby?
@1000millimeter @jonty it escalated a bit and maybe one day I earn the money I just invested in machines and key blanks?