These badges belonged to 4747461 Pte Victor Ernest Green of the Hallamshire Battalion during WW2, and his Father, 55492 Pte Ernest William Green 24th Bn Manchester Regt (previously 1808 1/7 Company Kent (Fortress) Royal Engineers), during WW1.
They were in a shoebox together with a variety of medals, paperwork and souvenirs from both WW1 and WW2.