Thanks for that link, I note from the "Researching Men" linked page that
"Researching a man who served in the Labour Corps can be a difficult task."
Quite so. I have found a Leonard Stanley Nash, aged 38+280 days who might be a relative of mine and his signup papers in the "burnt records", and it's not clear if he signed up to the 133rd Labour Coy, but seems to have been assigned to the 28th, but not until 1917 when he was moved from the Reserve. I can't see the second page with details of next of kin at present, so can't verify if it's him.
If anyone's researched him already, I'd be glad to hear.