His copy of the Daily Telegraph is mocked up and I'd imagine the rest of it probably is to as even if Ol' Blue Eyes was on the Tube, I don't think the London Underground would have had in-carriage displays back then. It looks like a fairly youthful picture of Sinatra.
However, apparently Frank Sinatra did have an interest in public transport to some extent. I was on a London Walk a few weeks ago and we stopped outside one of those little green black cab driver "houses". Our brill tour guide regaled us with the following urban myth. Frank Sinatra was staying in a fairly swanky hotel in London and saw a little green hut outside and wondered what it was.
When he heard that it was where cabbies had a rest and a cuppa, he demanded to be shown inside. The cabbies were fairly nonchalant when he walked in, and carried on reading papers as though Frank Sinatra visited them every day.
One of them asked what he did and Frank Sinatra said, "Well I sing a bit". "Hmm" said the cabbie, "Give us a song then". Frank proceded to belt out one of his tunes and the cabbie reportedly said "If I were you, I wouldn't take it up professionally". I imagine the taxi drivers lived off that story for some time, as it was a good one to add to their "I had that xxxxx celebrity in the back of my cab last week" stories.
I suppose it's quite fortunate that Tube drivers don't really get a chance to see the passengers they carry. Not that you would get that many instances of celebrities boarding the Tube and being asked to sing, or act, or do an impression.
However, this might happen if they travelled on the Jubilee Line. The infamous tube driver Richie seems to get a lot of fun watching the passengers and announcing what they're carrying on board. He invited passengers to have a bit of a sing-a-long in car number 4 as he saw someone with a guitar. Also car number five had a person with an ironing board and Richie saw this as an opportunity for people to get their ironing done.