To be sure, the Brits had different requirements, they could hop-scotch their way to the Far East, India and Australia, so that accounted for some of the choices when writing requirements.
Their main personnel transport in the 50s was the H.P. Hastings, a large four engine type and anachronistic tail-dragger based on the wartime Halifax bomber.
Smaller transports included the Vickers Valetta, which unbelievably had soars cutting through the cabin, again pretty old-school for the 50s.
The one area they did excel was the Argosy, a four engine twin boom turboprop..probably a bit more capable than the C-119. But by the time it was in widespread service, the C-130 had arrived and must have outperformed it as the Brita were early Hercules customers. Oddly, most civil customers for The Argosy were U.S. freight firms with DoD LOGAIR contracts....so in a way the U.S.military was a prime customer of the type.
The Belfast, like the C-133 was bought in modest numbers and remained in civil use after its military retirement. Unlike the C-133, I believe it was used as a troop transport. I haven't read the C-133 book and don't know why it wasn't used as a personnel transport...either it's safety concerns or with the C-141 on the drawing board it wasn't needed in that role.
Also, the RAF bought examples of UK airline types for personnel transport to overseas bases, notably the Brittania 4 engine turboprop and Andover twin-turboprop (which differed from civil variants by having a rear loading ramp) and of course the Comet.
My father flew '124s so I have a strong interest in the type. I have his Dash-1 and a large 1/72 metal desk model of it. I would have loved to fly in one, but I missed it by about a decade. But I did get to fly in '130s and '141s...a decent, but not as romantic, substitute.