Tracing someone who was in British Army in WW2?

My dad, who is no longer with us, was in the army during WW2 and I would like to find out more about what he did. He never spoke about it much when he was alive just that he was away in the army when his house at home was bombed and he lost his first wife and baby in the air raid. He went on to marry my mum some years after the war. Did the army keep any records and where can I start a search? I’d love to find out more if you can help me.
Thanks old lady! He was in the East Yorkshire Batalion. I have a photo of him with his colleagues.

STEVIE