...I'll check the book...
Right, Arthur Barnes (born 1828) retired in 1866 (aged 38) and became a landlord in Birmingham. Edward Barnes Crichton appears to have stopped travelling and returned to the UK in 1864. Harry Connor, who named Edward as a trustee in his will (for a while) was born in Dublin in 1821, worked most of his life in England and died in Essex in 1887 aged 66. I think it's safe to assume that Connor retired a few years befor Barnes because he was older, but I don't know.
Barnes and Connor were both champion somersaulters and were variously professional partners and friends over the years. It's clear from the book that there was no need at all for Edward to travel overseas if his livelihood
(whatever it was) relied on circuses/performers. There was a LOT of circus/pantomime activity in England throughout the 1850/60s and it was very popular. Celebrities like Barnes & Connor did travel abroad a but there was money to be made here so I think their attitude might have been "Why bother?" although there was some kudos to be earned by association with international circuses. Barnes had been all over Europe and the US.
I'm discounting the idea that Edward was a contortionist (at the moment) because nobody can find a reference to it and I think the photo was of someone else who Edward might have known. Maybe he just got to know the English circus people in foreign parts as compatriots, because he went to the circus, while he was doing his job
(whatever it was). Connor obviously knew him and trusted him.
The book mentions another book, "A History Of The Circus" by George Speaight which seems to be
THE book about err.. the history of the circus. Very interesting if you're interested in that sort of thing. I'll see if I can access it but I'm doubtful that Edward Barnes Crichton's name will appear.