Hi Tom.

It's an interesting one, but with the catalogues we have I'm not sure we are able to pin down the exact model for you.

The dial is very reminiscent of this 5408 from 1945:

The case looks similar too, but that 5408 has a 10.5 ligne movement, which is less than 24mm - given how the movement fits in your watch, I'd say we're not talking the same model, but a larger version thereof.

We also see from catalogues of this period that there are plated cases with steel casebacks, like this 342:

The dial has the wider version of the Heuer shield, so I'd agree that it's not one of the very early ones - somewhere from the late 30s to the mid 40s would be about right, I'd say. There seems to be at least two series of serial numbers in parallel at the time - if it's one of the 4xxxxx ones, low 450s and earlier are likely to be pre-war or during the war, higher 451s the post-war period. I don't have a good handle on these older serials though, so that's about as rough a guideline as you will get! The 7xxxxx serials I'm even less clear on...