Ok, let’s drag this back on topic. Your hours dispute with the company needs careful reading of your contract, and probably a specialist lawyer. If you can not do the job you are contracted for, the company is not under obligation to give you other work, nor pay you your full wages for any other work they can give you, if the hours are less. Unless such conditions are part of your contract. They may be ‘liable’ for your accident (how? Negligence? Bad practice? ) , but that does not mean they have to pay your wages for less hours worked.
As for the limited company agency route, unless you have lived on a cave, you should know what he score is.