Some years ago, I had an office in central London. One lunchtime I was walking down the street when I came face to face with the famous head of a TV Channel. He made eye contact and looked, for a split second, like he wanted to speak.

For some reason I never figured out, I put my face into neutral and passed him by. Perhaps I didn’t want to seem a ‘fan’, an ogler of the famous. I don’t know. And it was not the first time.

I once did that when I encountered Sir John Gielgud, even though I had always admired his work and even won an elocution contest at school by copying his delivery of a Cassius speech from Julius Caesar. He looked at me as I entered the cafe where he was sitting, and I passed him by without speaking.

What could I have said … “Oh Sir John, I’ve admired you for so long …” No. I don’t think so.

Fast forward a number of years to this very week. Monday morning started chilly, and I was striding through Mayfair in the early morning. Passing one of those discreet hotels in a side street, I noticed a doorman in full uniform, rubbing his hands against the chill. I caught his eye as I passed and smiled. He smiled back and his shoulders lifted immediately.

I was still feeling the pleasure of that fleeting exchange when I arrived at my destination. It made me beam at the receptionist, and she added a megawatt or two to her returning smile.

The doorman, the receptionist and I all had a great start to our days. Our spirits lifted, and I’m sure we all related better to those we met. Just because of that smile.

It was so easy to do. And it cost absolutely nothing.