The cap badge could be Royal Engineers, who in WW1 included Signals. If the letters within the wreath are GR, it will be Royal Engineers. If they are ASC you are right! I cannot read it clearly enough.
The badge on the forearm is a signaller's and the armband [or brassard] shows he was a dispatch rider. The upper arm badge may be a formation (division etc) sign.
As you say, the bandolier, breeches, spurs etc add up to mounted duties.
If you have the surname and initials or first name, they should show up on the National Archives documents online site - I cannot give the ref at present, or via Ancestry.