Records query

[Another Bubble]

At the outbreak of the Second World War, my Mum's Dad ran away from home with his best friend to join up.

They both had to lie about their age & occupation as they were both too young & both coal miners.

Part way through his training, my grandad realised the implications of what he'd done & wrote to his Mum, teling her what he'd done & where he was & asking her to come with his birth certificate to get him out. His friend still wanted to stay so asked my grandad not to say anything about him, so he didn't. My grandad went home to face the dangers that he was already familiar with & worked down the mines until he took early retirement in 1985, he married & had 7 children & 14 grandchildren. His friend got killed in action.

Is there any way I could find out which regiment he joined, albeit briefly, or would no such records exist? Asking him isn't an option as he died in 1993.