I think you will find that the Cathedral is not classed as a public building, but is owned by the Church of England, and due to the content of the game and the similarities of the actual Cathedral and the one in the game, the C of E are upset that they were not asked permission for the building to appear in the game. If they were asked, I bet it would have been a resounding no. People fail to remember the power that the religious orders of the world have.

The legal battle now will be for the Games Company (Sony - or its 3rd Party Contractor), to prove that the Cathedral in the game has similarities but is not that actual building. So things like changes to the spire, or different stained glass to the original, should allow the company to leave the structure in the game.

C of E will be more upset about the games content being used in their Cathedral, rather than a building belonging to them appearing in some bit of entertainment, and that permission was never sought.

I wonder if the internals have been modelled and included and are exact. Maybe Sony should have been more careful?