Unidentified Army badges

I'm wondering if there may be anyone who has knowledge of the British military who may be able to help me to identify these army badges?

They belonged to my father, who was in the Cheshire Regiment during World War II.

Dad didn't talk a lot about his time in the army and although he told me about these badges when I was a child, now I simply can't remember what he told me!

Foolishly, I must have believed that dad would live forever, and there would be another day to write down details of what he told me.

These three cloth badges are starting to show their years, as you can see. I also have three metal badges, again not knowing their significance. If anyone has any clues of what the badges are, I would appreciate any leads.