WWI Regiment No.

[ShaunJ]

This is the best I can do from the picture that was posted

[atom12]

Hi 

Judging by the shape of the cap badge - which is not showing up clearly, he could be with the Labour Corp.

[atom12]

Still think it is Labour Pioneer Corp cap badge:

[ShaunJ]

It does look like Labour Corps doesn't it. I can't think what else it could be.

There are only two William Dellers from the Labour Corps in the Medals Cards index:

Deller, William H H
Devonshire Regiment 30578(Incomplete) Acting Serjeant
Labour Corps 63282(Incomplete) Acting Serjeant

Medal card of Deller, William C V
Royal Engineers WR/4262(Incomplete) Pioneer
Labour Corps 34432(Incomplete) Pioneer

From what Matthew says it's unlikely to be either of them

[ShaunJ]

Useful site for Labour Corps research http://www.geocities.com/labour_corps/index.htm

[atom12]

He possibly did not venture abroad during WW1, if he did not go abroad he would not be on the medal rolls.   

Perhaps a visit to search the National Archives in person would be worthwhile.