On top of the obligatory 3D aspect, this time – get ready to roll your eyes – there are zombies. Rossio shrugs. “People might be cynical, but I think it’s consistent with the tone of the movies so far.

"We’ve had romance, humour, comedy, adventure, ghosts. We’ve had skeletons, pirates shooting people, monsters… We’re trying to make it macabre – scary but fun, instead of out-and-out gory. I know zombies seem a little overused, but they do fit with that ambition.”

The sceptics may sneer – as they did a few days before our visit when Depp turned up, unannounced and in full make-up, at a school in Greenwich after a nine-year-old girl wrote to ‘Captain Jack’, asking if he could lead a mutiny against her teachers.

Oh, how calculating! Think of the free publicity! Disney must have told him to do it…

“It was all Johnny’s idea,” says the unit publicist. Producer Jerry Bruckheimer concurs. “The letter moved him,” he says.

“It was fun for Johnny and great for her – a story she’ll tell for the rest of her life. Only around six people knew he was doing it. He wanted to keep it that way.

"But I guess one of the kids had a camera and took pictures...”