However, like most stories of the paranormal, there's a mundane fact that undermines the whole thing. Apparently the inner hull of the Great Eastern had inspection hatches. Even if the workmen had become trapped (the bit about the skeletons is rumor and in different versions of the story there's one skeleton or two, the skeleton is of a shipwright rather than a common worker, etc.), they could use the hatches to escape.
However, that doesn't mean you still can't have an interesting story. Here goes...
The workmen are briefly trapped inside, but use the hatches to escape. Them realizing they're trapped and trying to find a way out before they suffocate or overheat, with nobody able to hear their cries for help over the noise of the construction, could be a terrifying start for the tale. After they get out, they confront the foreman or even shipbuilder Isambard Brunel himself (the villain of the Sting song) over what happened. Fearing the bad publicity, worker unrest, etc. this could cause (according to the song Brunel was rushing construction), Brunel has a couple goons kidnap the two men and take them to some faraway place and dump them. He reckons it will take them a long time to get home and the ship will be finished and launched by then, so even if they do manage to raise a stink, it won't be a major problem.
One of the workers--perhaps unhinged by claustrophobia during his entrapment or by the pounding of the hammers (that the two hulls would amplify)--makes his way back to the Great Eastern in time for it to launch. He hides inside the double hull and commits various acts of sabotage over the years like a sort of working-class Phantom of the Opera,starting with the death of Brunel himself. You could throw in some class envy and poverty by depicting him sneaking out of his lair and eating the kind of luxurious ocean-liner food he could never afford as a Victorian industrial worker. If you want to go with the "skeleton found in the hull" aspect of the legend, perhaps he's killed as the result of one of his sabotages or in some other sort of mishap (like the time the hull got gashed at sea) and his body is found when the ship is broken up, thus spawning the legend.
You like? It's a "rational explanation" for an apparent haunting (hence the title of this post) but still touches on things like workplace safety, the rich and powerful being above the law, poverty, etc. Between my graduate school obligations and higher-priority projects I can't write this one, so if you think you can make a go of this, feel free to write it.
I'd like some kind of acknowledgement though. :)