And yet somehow the output per man was still higher than in the "highly mechanised" American shipyards. Even the Liberty ships were never really production-line items: you aren't making every single example of a particular ship frame in one factory, on one jig, where the workers do that and nothing else all day long. That means you lose a lot of the benefits flowing from economies of scale - the huge production figures at the US shipyards were largely achieved by throwing huge numbers of workers at them. A highly skilled shipwright with a hammer, for instance, will be able to produce higher quality rivets than a semi-skilled one with a pneumatic hammer: this is important because poor quality rivets may have to be drilled out and refitted, a time consuming and expensive process, or you have to overdesign the ship with far too many rivets which again causes you to waste build time.Well, finally you have admitted that British shipyards were outdated. You know, they even lacked pneumatic and electric tooling, as well as electric welding tools. Maybe even big yards like Vickers or A-W or Beardmore or H&W.
Welding is a separate issue - the UK was behind there, but the probably not by all that much and given the timing of the depression any transition to welded hulls is very difficult to justify.