‘Have a good evening, ladies,’ he said.

‘Thank you very much,’ Ginger said. ‘You too.’

We kept moving.

‘You know the room number?’ Ginger said.

‘He sent me a text.’

Three innocuous numbers. That was all. Numbers that would mean nothing to someone who saw them by accident. He had it all worked out, the rotten bastard.

Ginger began heading towards the main entrance but I stopped her. The Langham has a side door for the hotel restaurant and bar, and that’s the one we took. It is much more private. No top-hatted doormen, fewer guests coming and going. But the bar was crowded. We crossed the lobby where a security guard in a dark suit hovered by the lift, his eyes evaluating us for a poker-faced professional beat – me in my Stella McCartney jacket and Ginger in her casual-but-chic Sweaty Betty active wear – before he smiled deferentially and held the lift door open for us.

‘Ladies,’ he said. ‘Have a good night.’

We went up to the top floor.

The lift door closed behind us and the noise and bustle of the ground floor suddenly felt light years away. The corridor on the top floor was empty apart from room service trolleys and dinner trays that had been left outside some of the doors. We started down the corridor and, as we turned a corner, a shadow disappeared into the service lift. We paused for a moment, listening to the hotel hush, and then walked to James Caine’s door.

A piano sonata was playing softly inside. Do not disturb, red LED lights said on the frame of the door.

Ginger rang the bell.

No reply.

‘He’s probably got some woman in there.’ Ginger said. ‘Open up, creep!’

She banged on the door.

‘He’s not in there,’ I said. ‘Let’s go home, Ginger.’

‘Oh, he’s in there,’ she said, giving the door a sharp kick.

And it opened. By no more than an inch, but the piano sonata was suddenly much louder. Ginger and I stared at each other and then she very gently pushed the door open as far as it would go.

‘Hey!’ she called, but not quite so bold now.

No response. Ginger hesitated for a moment and then went inside.

I glanced up and down the empty corridor, and then I followed her.

The room was pristine in its fussy neatness, as if the maid had only just done her evening rounds, turning the sheets back on the bed, placing a complimentary chocolate on the pillow, replenishing the fruit bowl of a favoured guest. The sound of Ludovico Einaudi tinkling the ivories came from the massive HDTV.

The bathroom door was open, all lights blazing, and there were fresh white towels that had never been touched.

It was as if the room was still waiting for its occupant.

And then Ginger cried out. Not loud. Hardly a sound at all. More of a sharp inhalation of total and dumbfounded disbelief.

She stood with her hands over her mouth as I went to her side and stared down at the space between the sofa and the big HDTV where the dead man was lying on his back.