I have checked Ancestry and cannot find a Hugh Cecil Walker serving in WW1. There are quite a few Hugh Walker's in the Medal Card Index. But until we can establish what the cap badge is we are clutching at straws, so to speak.
It was not uncommon for Birmingham men to serve in various regiments all round the country. Born in 1881 he would have been 33/34 when WW1 started. So he may have been conscripted during later half of war when married men under a certain age were called up. And if that happened you had little choice of what regiment. You were sent were you where needed most.
If you know where he lived, howabout, checking the Absent Voters Book, for 1918. I am sure a forum member can do that
Terry