I’ve seen options come up on Connected Opportunity cards to change which faction one is closest to after the decision from the Numismatrix storyline, but on the Constables card, there doesn’t seem to be a option visible for choosing them as a side, though there is for betraying them. So, is the Numismatrix the only chance a character has for choosing to be closest to them? I couldn’t find anything else on the wiki.
No, there should be one for “turning nark of a criminal friend,” requiring Ruthless and a Use of Villains on the Constables’ card to become Closest To: them. I don’t thin kit relies on the Airs of London to become visible, but I might be mistaken.
Unlike becoming Closest To: Criminals, it is not dependent upon your choice between the Last Constable and the Cheery Man, so I’m not sure why it was not visible to you. If I draw it again in a timely manner, I’ll verify it hasn’t disappeared in the last couple of days…